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. B, Solid state

Random-field instability of the ferromagnetic state

T. Schneider, Erling Pytte

Published Feb 1, 1977• 225 citations
Publisher

Abstract

We consider an Ising model with infinite-ranged interaction with statistically independent site fields with Gaussian distribution. The model is solved exactly and exhibits both an independent spin phase and a ferromagnetic phase, separated by a line of second-order phase transitions. We also establish that the replica technique yields exact results in the present model but not in the related random exchange system.

DOI
10.1103/physrevb.15.1519

Related papers

First-order phase transition in a 2D random-field Ising model with conflicting dynamics

Nuno Crokidakis

The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbor interactions. In order to generate the random magnetic fields, we have considered random variables { h } that change randomly with time according to a double-Gaussian probability distribution, which consists of two single-Gaussian distributions, centered at + h o and − h o , with the same width σ. This distribution is very general and can recover in appropriate limits the bimodal distribution ( ) and the single-Gaussian one ( h o = 0). We performed Monte Carlo simulations in lattices with linear sizes in the range L = 32–512. The system exhibits ferromagnetic and paramagnetic steady states. Our results suggest the occurrence of first-order phase transitions between the above-mentioned phases at low temperatures and large random-field intensities h o for some small values of the width σ. By means of finite size scaling, we estimate the critical exponents in the low-field region, where we have continuous phase transitions. In addition, we show a sketch of the phase diagram of the model for some values of σ.

arXiv:0901.2659•Journal of Statistical Mechanics Theory and Experiment•Feb 24, 2009•7 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

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

E. Nogueira, Fernando Dantas Nobre, S. Coutinho +1 more

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.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 1, 1996•1 citation

Limit distribution of an infinite-range random Ising model

D. Wagner

The limit distribution of a random Ising model (site disorder) with an exchange interaction of infinite range is calculated exactly. It is shown that randomness changes the analytic properties of the limit distribution at the critical point considerably. At criticality this system cannot be described by a Hamiltonian which is a polynomial in the spin variables.

Journal of Physics A Mathematical and General•Oct 1, 1982•1 citation

TWO-DIMENSIONAL ISING MODEL IN ANNEALED RANDOM FIELDS

L.L. Gonçalves, Tomoya Horiguchi

The critical behaviour of the two-dimensional Ising model in annealed random fields is studied. Two different kinds of random field are considered and exact results obtained for the transition temperature when the field distribution is symmetric. In the first case the random field is unrestricted and the explicit results obtained for discrete and gaussian field distributions show the annealed field favours the ordering of the system. In the second case the random field satisfies a constraint and explicit results are also obtained for discrete and gaussian field distributions. In the discrete distribution the field assumes the values ±h0,0 and it is shown that there is a critical field hc such that for h0>hc the system presents a reentrant phase transition. In this case the ferromagnetic ground state becomes unstable and there is the appearance of a superantiferromagnetic phase. For h0<hc the ferromagnetic state is stable and the transition temperature decreases due to the presence of the random field.

International Journal of Modern Physics B•Aug 1, 1990•2 citations
We consider an Ising model with infinite-ranged interaction with statistically independent site fields with Gaussian distribution. The model is solved exactly and exhibits both an independent spin phase and a ferromagnetic phase, separated by a line of second-order phase transitions. We also establish that the replica technique yields exact results in the present model but not in the related random exchange system.
The effects of locally random magnetic fields are considered in a nonequilibrium Ising model defined on a square lattice with nearest-neighbor interactions. In order to generate the random magnetic fields, we have considered random variables { h } that change randomly with time according to a double-Gaussian probability distribution, which consists of two single-Gaussian distributions, centered at + h o and − h o , with the same width σ. This distribution is very general and can recover in appropriate limits the bimodal distribution ( ) and the single-Gaussian one ( h o = 0). We performed Monte Carlo simulations in lattices with linear sizes in the range L = 32–512. The system exhibits ferromagnetic and paramagnetic steady states. Our results suggest the occurrence of first-order phase transitions between the above-mentioned phases at low temperatures and large random-field intensities h o for some small values of the width σ. By means of finite size scaling, we estimate the critical exponents in the low-field region, where we have continuous phase transitions. In addition, we show a sketch of the phase diagram of the model for some values of σ.
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 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 critical behaviour of the two-dimensional Ising model in annealed random fields is studied. Two different kinds of random field are considered and exact results obtained for the transition temperature when the field distribution is symmetric. In the first case the random field is unrestricted and the explicit results obtained for discrete and gaussian field distributions show the annealed field favours the ordering of the system. In the second case the random field satisfies a constraint and explicit results are also obtained for discrete and gaussian field distributions. In the discrete distribution the field assumes the values ±h0,0 and it is shown that there is a critical field hc such that for h0>hc the system presents a reentrant phase transition. In this case the ferromagnetic ground state becomes unstable and there is the appearance of a superantiferromagnetic phase. For h0<hc the ferromagnetic state is stable and the transition temperature decreases due to the presence of the random field.