On the mean-field Ising model in a random external field

1985 ◽  
Vol 41 (1-2) ◽  
pp. 299-313 ◽  
Author(s):  
S. R. Salinas ◽  
W. F. Wreszinski
Keyword(s):  
Ising Model ◽  
External Field ◽  
Mean Field ◽  
The Mean ◽  
Random External Field

Single-Crystal Magnetic Properties of [Co(NH3)5(OH2)] [Cr(CN)6] Between 2 and 300 K

1992 ◽  
Vol 45 (11) ◽  
pp. 1899 ◽  
Author(s):  
PA Reynolds ◽  
CD Delfs ◽  
BN Figgis ◽  
B Moubaraki ◽  
KS Murray
Keyword(s):  
Ising Model ◽  
Field Model ◽  
Mean Field ◽  
Zero Field ◽  
Spin Orbit Coupling ◽  
Zero Field Splitting ◽  
Magnetic Exchange Interaction ◽  
Mean Field Model ◽  
Magnetic Exchange ◽  
The Mean

The magnetic susceptibilities along and perpendicular to the c axis (hexagonal setting) between 2.0 and 300 K at a magnetic field of 1.00 T, and the magnetizations at field strengths up to 5.00 T, are presented for single crystals of [Co(NH3)5(OH2)] [Cr(CN)6]. The results are interpreted in terms of zero-field splitting (2D) of the ground 4A2g term by spin-orbit coupling and of magnetic exchange interaction between the chromium atoms. The magnetic exchange is modelled as one of Ising or mean-field in type. The exchange is found to be quite small: J = -0.18(6) cm-1 if the Ising model is employed, and -0.03(1) cm-1 for the mean-field model. The model adopted for the exchange has a strong influence on the value of the parameter D obtained. When the Ising model is used D is deduced to be -0.28(9) cm-l; when the mean-field model is used D is -0.14(4) cm-l. The g-values deduced are in agreement with those from e.s.r. measurements at higher temperatures and do not depend on the exchange model. In any case, D is found to be sufficiently large that it must be considered in a polarized neutron diffraction experiment on the compound.

Analytical solution of the mean field Ising model for finite systems

2012 ◽  
Vol 24 (22) ◽  
pp. 226004 ◽  
Author(s):  
Dalía S Bertoldi ◽  
Eduardo M Bringa ◽  
E N Miranda
Keyword(s):  
Ising Model ◽  
Analytical Solution ◽  
Mean Field ◽  
Finite Systems ◽  
The Mean

scholarly journals Generalization of the mean-field Ising model within Tsallis thermostatistics

1997 ◽  
Vol 238 (1-4) ◽  
pp. 285-294 ◽  
Author(s):  
Fevzi Büyükkiliç ◽  
Doǧan Demirhan ◽  
Uǧur Tirnakli
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
The Mean

Phase Transitions and the Ising Model

2019 ◽  
pp. 423-446
Author(s):  
Robert H. Swendsen
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Landau Theory ◽  
Magnetic Moments ◽  
Mean Field ◽  
Higher Dimensions ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ising Chain ◽  
The Mean

Chapter 17 presented one example of a phase transition, the van der Waals gas. This chapter provides another, the Ising model, a widely studied model of phase transitions. We first give the solution for the Ising chain (one-dimensional model), including the introduction of the transfer matrix method. Higher dimensions are treated in the Mean Field Approximation (MFA), which is also extended to Landau theory. The Ising model is deceptively simple. It can be defined in a few words, but it displays astonishingly rich behavior. It originated as a model of ferromagnetism in which the magnetic moments were localized on lattice sites and had only two allowed values.

The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model

1997 ◽  
Vol 11 (13) ◽  
pp. 565-570
Author(s):  
G. L. S. Paula ◽  
W. Figueiredo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Stationary States ◽  
Transition Rates ◽  
The Mean ◽  
The One

We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

scholarly journals Renewal properties of the d = 1 Ising model

2018 ◽  
Vol 30 (09) ◽  
pp. 1850018
Author(s):  
Marzio Cassandro ◽  
Immacolata Merola ◽  
Errico Presutti
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Renewal Process ◽  
Infinite Sequence ◽  
Mean Field ◽  
Coarse Graining ◽  
Inverse Temperature ◽  
Scaling Parameter ◽  
Kac Potentials ◽  
The Mean

We consider the [Formula: see text] Ising model with Kac potentials at inverse temperature [Formula: see text] where the mean field predicts a phase transition with two possible equilibrium magnetizations [Formula: see text], [Formula: see text]. We show that when the Kac scaling parameter [Formula: see text] is sufficiently small, typical spin configurations are described (via a coarse graining) by an infinite sequence of successive plus and minus intervals where the empirical magnetization is “close” to [Formula: see text], and respectively, [Formula: see text]. We prove that the corresponding marginal of the unique DLR measure is a renewal process.

scholarly journals Censored Glauber Dynamics for the Mean Field Ising Model

2009 ◽  
Vol 137 (3) ◽  
pp. 407-458 ◽  
Author(s):  
Jian Ding ◽  
Eyal Lubetzky ◽  
Yuval Peres
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Glauber Dynamics ◽  
The Mean
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