Physical review. B, Condensed matter

Spin-glass transition in three-dimensional random-anisotropy-axis model

Amitabha Chakrabarti

Published Oct 1, 1987• 15 citations

Abstract

The critical behavior of the three-dimensional random-anisotropy-axis model is studied by Monte Carlo simulations in the limit of infinite anisotropy. Finite-size scaling analysis of the data for equilibrium averages strongly indicates a finite-temperature phase transition. The values of the critical exponents are similar to those found for the three-dimensional short-range Ising spin glass.

DOI: 10.1103/physrevb.36.5747

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Spin-glass transition in the random anisotropy axis model

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Results of computer simulations on random-anisotropy-axis model (RAM) are reported in the limit of infinite anisotropy. Finite-size scaling analyses of the data for equilibrium averages indicates a zero-temperature phase transition in two dimensions. The critical exponents are similar to those found for short-range Ising-spin-glass models in two dimensions. These results support the argument that RAM and short-range Ising spin-glass models belong to the same universality classes.

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Physical review. B, Condensed matter

Spin-glass transition in three-dimensional random-anisotropy-axis model

Amitabha Chakrabarti

Published Oct 1, 1987• 15 citations

Publisher

Abstract

DOI: 10.1103/physrevb.36.5747

Related papers

Spin-glass transition in the random anisotropy axis model

Amitabha Chakrabarti

The critical behavior of the Random Anisotropy Axis model (RAM) is studied by the Monte Carlo simulation method in the limit of infinite anisotropy. Finite size scaling analysis of the data for equilibrium averages strongly suggests a zero temperature critical point in two dimensions and a finite temperature phase transition in three dimensions. The values of the critical exponents in both two and three dimensions indicate that RAM belongs to the same universality class as that of short-range Ising spin-glass models.The critical behavior of the Random Anisotropy Axis model (RAM) is studied by the Monte Carlo simulation method in the limit of infinite anisotropy. Finite size scaling analysis of the data for equilibrium averages strongly suggests a zero temperature critical point in two dimensions and a finite temperature phase transition in three dimensions. The values of the critical exponents in both two and three dimensions indicate that RAM belongs to the same universality class as that of short-range Ising spin-glass models.

Journal of Applied PhysicsApr 15, 19887 citations

Phase transition in random-anisotropy magnets

Amitabha Chakrabarti

Physical review. B, Condensed matterFeb 1, 19892 citations

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Takayuki Shirakura, Fumitaka Matsubara

We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D $\mp J$ Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.We study a short-range site-random Ising model in three dimensions (3D) using a Monte Carlo (MC) method and find a phase transition to a spin glass (SG) phase at a very high temperature ( T c ≃2.83 J). Values of the critical exponents estimated from a finite-size scaling analysis are different from those in both the 3D$\mp J$ Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.

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Phase transition in the three-dimensional ±J Ising spin glass

Naoki Kawashima, A. P. Young

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We present results of a Monte Carlo simulation study of the zero-temperature quantum phase transition of a three-dimensional short-range spin-1/2 Ising spin glass, driven by a transverse magnetic field. This quantum transition is equivalent to the finite-temperature transition in the (3+1)-dimensional anisotropic classical random Ising model that is the path integral of the quantum system. The critical exponents are estimated using a finite-size scaling analysis. The uniform linear susceptibility is finite at the transition, while the nonlinear susceptibility diverges. The results are more consistent with conventional, rather than activated, dynamic scaling in the quantum system.We present results of a Monte Carlo simulation study of the zero-temperature quantum phase transition of a three-dimensional short-range spin-1/2 Ising spin glass, driven by a transverse magnetic field. This quantum transition is equivalent to the finite-temperature transition in the (3+1)-dimensional anisotropic classical random Ising model that is the path integral of the quantum system. The critical exponents are estimated using a finite-size scaling analysis. The uniform linear susceptibility is finite at the transition, while the nonlinear susceptibility diverges. The results are more consistent with conventional, rather than activated, dynamic scaling in the quantum system.

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R. N. Bhatt, A. P. Young

The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having \ifmmode\pm\else\textpm\fi{}J distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3\ensuremath{\le}L\ensuremath{\le}20. Results for the probability distribution, ${\mathrm{P}}_{\mathrm{L}}$ (q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at ${\mathrm{T}}_{\mathrm{c}}$ ${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.The three-dimensional Ising spin-glass in zero field with nearest-neighbor interactions having \ifmmode\pm\else\textpm\fi{}J distribution is studied by Monte Carlo simulations for samples of linear dimension L with 3\ensuremath{\le}L\ensuremath{\le}20. Results for the probability distribution, ${\mathrm{P}}_{\mathrm{L}}$(q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at ${\mathrm{T}}_{\mathrm{c}}$${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.

Physical Review LettersMar 4, 1985392 citations

\mp J

Ising model and the 3D Ising ferromagnet. We suggest that the SG phase in this model is a new SG phase which is characterized by a nonzero SG order parameter q ≠0.

{T}_{c}

with ordering below

{T}_{c}

. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent $\ensuremath{\nu}$ is somewhat higher. Because there may be (unknown) corrections to finite-size scaling, we do not completely rule out the possibility that

{T}_{c}=0

or that

{T}_{c}

is finite but with no order below

{T}_{c}

. However, from our data, these possibilities seem less likely.

{\mathrm{P}}_{\mathrm{L}}

(q), of the spin-glass order parameter are analyzed by finite-size scaling. Data for T\ensuremath{\ge}1.2 are consistent with a conventional phase transition at

{\mathrm{T}}_{\mathrm{c}}

${=1.2}_{\mathrm{\ensuremath{-}}0.2}^{+0.1}$, with exponents \ensuremath{\nu}=1.3\ifmmode\pm\else\textpm\fi{}0.3 and \ensuremath{\eta}=-0.3\ifmmode\pm\else\textpm\fi{}0.2. However, results at lower temperature indicate marginal behavior and suggest that the lower critical dimensional is close to three.