Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

m-vector spin glass in the presence of a Gaussian random field

E. Nogueira, Fernando Dantas Nobre, S. Coutinho, J. R. L. de Almeida

Published Jun 1, 1996• 1 citation
Publisher

Abstract

The infinite-range m-vector spin glass in the presence of a Gaussian random field (characterized by a mean ${\mathit{h}}_{0}$ and width \ensuremath{\Delta}) is investigated through the replica method. The phase diagram of the model, for ${\mathit{h}}_{0}$=0 and \ensuremath{\Delta} finite, is obtained within replica-symmetry approximation. It is shown that the paramagnetic phase is enhanced, contrary to what happens to the spin-glass, mixed-ferromagnetic, and ferromagnetic phases, for growing values of \ensuremath{\Delta}. For ${\mathit{h}}_{0}$\ensuremath{\ne}0, the changes introduced in the Gabay-Toulouse line by finite values of \ensuremath{\Delta} are investigated. In particular, it is shown that the critical exponent characteristic of the Gabay-Toulouse line is nonuniversal, changing continuously with the distribution width \ensuremath{\Delta}. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.53.5742

Related papers

Quantum vector spin glasses with random Dzyaloshinsky-Moriya interactions

T. K. Kopeć, G. Büttner

The infinite-range quantum vector spin glass with random Dzyaloshinsky-Moriya anisotropy (with variances J and D for random bonds and anisotropy, respectively) and external magnetic field (h) is studied by means of the thermofield dynamics as a substitute for the replica method for the spin values S=1/2, 1, and 3/2. The temperature-anisotropy phase diagrams have been calculated numerically for arbitrary anisotropy and different values of the applied magnetic field h. The stability analysis of the mean-field-type solution against the action of fluctuations has been performed, leading to the upper and lower critical lines in the field-temperature plane. For small values of the reduced anisotropy variance d=D/J (0.1d0.3), we find a crossover of the upper critical line from the de Almeida--Thouless (AT) -type behavior [${\mathit{T}}_{\mathit{c}}$(h)\ensuremath{\propto}${\mathit{h}}^{2/3}$] for small fields to the Gabay-Toulouse (GT) -like behavior [${\mathit{T}}_{\mathit{c}}$(h)\ensuremath{\propto}${\mathit{h}}^{2}$] for large fields. For larger anisotropies (d\ensuremath{\ge}0.3) the upper critical line is essentially that of the AT type. Interestingly, the lower critical line, which persists for d0.5, exhibits the reverse type of behavior for the corresponding values of the anisotropy d. Additionally, we have analyzed transverse and longitudinal susceptibilities for different values of the field h. We found that a small amount of the anisotropy d stabilizes a plateau of the local susceptibilities in the spin-glass phase.

Physical review. B, Condensed matter•May 1, 1991•13 citations

Effects of a Gaussian random field in the Sherrington-Kirkpatrick spin glass

R. F. Soares, Fernando Dantas Nobre, J. R. L. de Almeida

The infinite-range Ising spin glass in the presence of a Gaussian random field is investigated by means of the replica method. The replica-symmetric solution and its instability are discussed; it is shown that the Almeida-Thouless instability regions are always reduced by the random field. The crossover exponent \ensuremath{\varphi} associated with the irreversibility line is shown to be nonuniversal in the presence of a random field, varying in a range from 1 to 3. Some of our results are compared with recent experimental measurements performed in the diluted antiferromagnet ${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{F}}_{2}$.

Physical review. B, Condensed matter•Sep 1, 1994•32 citations

Model of a quasi-one-dimensional spin glass

Matej Orešič, R. Pirc

We consider a system of linear chains of Ising spins with short-range nearest-neighbor ferromagnetic interactions of strength K along the chains, and with infinite-range random interchain interactions of a Sherrington-Kirkpatrick type. Also included in the model is a local Gaussian random field with variance \ensuremath{\Delta}. In the replica symmetric case, the system is mapped exactly on the one-dimensional Ising model in a random field and a recursion method for calculating the spin-correlation functions is developed. For \ensuremath{\Delta}=0, an analytic relation for freezing temperature ${\mathit{T}}_{\mathit{f}}$(K) is obtained. The replica-symmetric spin-glass phase is shown to be stable above the freezing temperature ${\mathit{T}}_{\mathit{f}}$(K,\ensuremath{\Delta}), which is determined numerically.

Physical review. B, Condensed matter•Feb 1, 1993•16 citations

Phase Diagram of the p-Spin-Interacting Spin Glass with Ferromagnetic Bias and a Transverse Field in the Infinite- p Limit

Tomoyuki Obuchi, Hidetoshi Nishimori, David Sherrington

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

arXiv:cond-mat/0611168•Journal of the Physical Society of Japan•May 11, 2007•22 citations

Nonlinear susceptibility of a quantum spin glass under uniform transverse and random longitudinal magnetic fields

S. G. Magalhães, C.V. Morais, Fábio M. Zimmer +2 more

The interplay between quantum fluctuations and disorder is investigated in a quantum spin-glass model, in the presence of a uniform transverse field $\mathrm{\ensuremath{\Gamma}}$, as well as of a longitudinal random field ${h}_{i}$, which follows a Gaussian distribution characterized by a width proportional to $\mathrm{\ensuremath{\Delta}}$. The interactions are infinite-ranged, and the model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure; in addition, the dependence of the Almeida-Thouless eigenvalue ${\ensuremath{\lambda}}_{\mathrm{AT}}$ (replicon) on the applied fields is analyzed. This study is motivated by experimental investigations on the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility ${\ensuremath{\chi}}_{3}$, which have led to a considerable experimental and theoretical debate. We have analyzed two physically distinct situations, namely, $\mathrm{\ensuremath{\Delta}}$ and $\mathrm{\ensuremath{\Gamma}}$ considered as independent, as well as these two quantities related, as proposed recently by some authors. In both cases, a spin-glass phase transition is found at a temperature ${T}_{f}$, with such phase being characterized by a nontrivial ergodicity breaking; moreover, ${T}_{f}$ decreases by increasing $\mathrm{\ensuremath{\Gamma}}$ towards a quantum critical point at zero temperature. The situation where $\mathrm{\ensuremath{\Delta}}$ and $\mathrm{\ensuremath{\Gamma}}$ are related $[\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}\mathrm{\ensuremath{\Delta}}(\mathrm{\ensuremath{\Gamma}})]$ appears to reproduce better the experimental observations on the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound, with the theoretical results coinciding qualitatively with measurements of the nonlinear susceptibility ${\ensuremath{\chi}}_{3}$. In this later case, by increasing $\mathrm{\ensuremath{\Gamma}}$ gradually, ${\ensuremath{\chi}}_{3}$ becomes progressively rounded, presenting a maximum at a temperature ${T}^{*}$ $({T}^{*}>{T}_{f})$, with both the amplitude of the maximum and the value of ${T}^{*}$ decreasing gradually. Moreover, we also show that the random field is the main responsible for the smearing of the nonlinear susceptibility, acting significantly inside the paramagnetic phase, leading to two regimes delimited by the temperature ${T}^{*}$, one for ${T}_{f}<T<{T}^{*}$, and another one for $T>{T}^{*}$. It is argued that the conventional paramagnetic state corresponds to $T>{T}^{*}$, whereas the temperature region ${T}_{f}<T<{T}^{*}$ may be characterized by a rather unusual dynamics, possibly including Griffiths singularities.

arXiv:1701.04373•Physical review. B./Physical review. B•Feb 1, 2017•6 citations

Phase diagram of the random energy model with ferromagnetic bias in the presence of a transverse field

Tomoyuki Obuchi, Hidetoshi Nishimori

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p \to \infty$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

•Nov 7, 2006•0 citations
The infinite-range m-vector spin glass in the presence of a Gaussian random field (characterized by a mean h0{\mathit{h}}_{0}h0​ and width \ensuremath{\Delta}) is investigated through the replica method. The phase diagram of the model, for h0{\mathit{h}}_{0}h0​=0 and \ensuremath{\Delta} finite, is obtained within replica-symmetry approximation. It is shown that the paramagnetic phase is enhanced, contrary to what happens to the spin-glass, mixed-ferromagnetic, and ferromagnetic phases, for growing values of \ensuremath{\Delta}. For h0{\mathit{h}}_{0}h0​\ensuremath{\ne}0, the changes introduced in the Gabay-Toulouse line by finite values of \ensuremath{\Delta} are investigated. In particular, it is shown that the critical exponent characteristic of the Gabay-Toulouse line is nonuniversal, changing continuously with the distribution width \ensuremath{\Delta}. \textcopyright{} 1996 The American Physical Society.
The infinite-range quantum vector spin glass with random Dzyaloshinsky-Moriya anisotropy (with variances J and D for random bonds and anisotropy, respectively) and external magnetic field (h) is studied by means of the thermofield dynamics as a substitute for the replica method for the spin values S=1/2, 1, and 3/2. The temperature-anisotropy phase diagrams have been calculated numerically for arbitrary anisotropy and different values of the applied magnetic field h. The stability analysis of the mean-field-type solution against the action of fluctuations has been performed, leading to the upper and lower critical lines in the field-temperature plane. For small values of the reduced anisotropy variance d=D/J (0.1d0.3), we find a crossover of the upper critical line from the de Almeida--Thouless (AT) -type behavior [Tc{\mathit{T}}_{\mathit{c}}Tc​(h)\ensuremath{\propto}h2/3{\mathit{h}}^{2/3}h2/3] for small fields to the Gabay-Toulouse (GT) -like behavior [Tc{\mathit{T}}_{\mathit{c}}Tc​(h)\ensuremath{\propto}h2{\mathit{h}}^{2}h2] for large fields. For larger anisotropies (d\ensuremath{\ge}0.3) the upper critical line is essentially that of the AT type. Interestingly, the lower critical line, which persists for d0.5, exhibits the reverse type of behavior for the corresponding values of the anisotropy d. Additionally, we have analyzed transverse and longitudinal susceptibilities for different values of the field h. We found that a small amount of the anisotropy d stabilizes a plateau of the local susceptibilities in the spin-glass phase.
The infinite-range Ising spin glass in the presence of a Gaussian random field is investigated by means of the replica method. The replica-symmetric solution and its instability are discussed; it is shown that the Almeida-Thouless instability regions are always reduced by the random field. The crossover exponent \ensuremath{\varphi} associated with the irreversibility line is shown to be nonuniversal in the presence of a random field, varying in a range from 1 to 3. Some of our results are compared with recent experimental measurements performed in the diluted antiferromagnet Fex{\mathrm{Fe}}_{\mathit{x}}Fex​${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$F2{\mathrm{F}}_{2}F2​.
We consider a system of linear chains of Ising spins with short-range nearest-neighbor ferromagnetic interactions of strength K along the chains, and with infinite-range random interchain interactions of a Sherrington-Kirkpatrick type. Also included in the model is a local Gaussian random field with variance \ensuremath{\Delta}. In the replica symmetric case, the system is mapped exactly on the one-dimensional Ising model in a random field and a recursion method for calculating the spin-correlation functions is developed. For \ensuremath{\Delta}=0, an analytic relation for freezing temperature Tf{\mathit{T}}_{\mathit{f}}Tf​(K) is obtained. The replica-symmetric spin-glass phase is shown to be stable above the freezing temperature Tf{\mathit{T}}_{\mathit{f}}Tf​(K,\ensuremath{\Delta}), which is determined numerically.
The phase diagram of the ppp-spin-interacting spin glass model in a transverse field is investigated in the limit p→∞p \to \inftyp→∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p→∞p \to \inftyp→∞ by using the large-ppp expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.
The interplay between quantum fluctuations and disorder is investigated in a quantum spin-glass model, in the presence of a uniform transverse field $\mathrm{\ensuremath{\Gamma}}$, as well as of a longitudinal random field hi{h}_{i}hi​, which follows a Gaussian distribution characterized by a width proportional to $\mathrm{\ensuremath{\Delta}}$. The interactions are infinite-ranged, and the model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure; in addition, the dependence of the Almeida-Thouless eigenvalue ${\ensuremath{\lambda}}_{\mathrm{AT}}$ (replicon) on the applied fields is analyzed. This study is motivated by experimental investigations on the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility ${\ensuremath{\chi}}_{3}$, which have led to a considerable experimental and theoretical debate. We have analyzed two physically distinct situations, namely, $\mathrm{\ensuremath{\Delta}}$ and $\mathrm{\ensuremath{\Gamma}}$ considered as independent, as well as these two quantities related, as proposed recently by some authors. In both cases, a spin-glass phase transition is found at a temperature Tf{T}_{f}Tf​, with such phase being characterized by a nontrivial ergodicity breaking; moreover, Tf{T}_{f}Tf​ decreases by increasing $\mathrm{\ensuremath{\Gamma}}$ towards a quantum critical point at zero temperature. The situation where $\mathrm{\ensuremath{\Delta}}$ and $\mathrm{\ensuremath{\Gamma}}$ are related $[\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}\mathrm{\ensuremath{\Delta}}(\mathrm{\ensuremath{\Gamma}})]$ appears to reproduce better the experimental observations on the ${\mathrm{LiHo}}_{x}{\mathrm{Y}}_{1\ensuremath{-}x}{\mathrm{F}}_{4}$ compound, with the theoretical results coinciding qualitatively with measurements of the nonlinear susceptibility ${\ensuremath{\chi}}_{3}$. In this later case, by increasing $\mathrm{\ensuremath{\Gamma}}$ gradually, ${\ensuremath{\chi}}_{3}$ becomes progressively rounded, presenting a maximum at a temperature T∗{T}^{*}T∗ (T∗>Tf)({T}^{*}>{T}_{f})(T∗>Tf​), with both the amplitude of the maximum and the value of T∗{T}^{*}T∗ decreasing gradually. Moreover, we also show that the random field is the main responsible for the smearing of the nonlinear susceptibility, acting significantly inside the paramagnetic phase, leading to two regimes delimited by the temperature T∗{T}^{*}T∗, one for Tf<T<T∗{T}_{f}<T<{T}^{*}Tf​<T<T∗, and another one for T>T∗T>{T}^{*}T>T∗. It is argued that the conventional paramagnetic state corresponds to T>T∗T>{T}^{*}T>T∗, whereas the temperature region Tf<T<T∗{T}_{f}<T<{T}^{*}Tf​<T<T∗ may be characterized by a rather unusual dynamics, possibly including Griffiths singularities.
The phase diagram of the ppp-spin-interacting spin glass model in a transverse field is investigated in the limit p→∞p \to \inftyp→∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p→∞p \to \inftyp→∞ by using the large-ppp expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.