Two-dimensional Ising model with annealed random fields (original) (raw)

Finite-temperature phase transition in the two-dimensional randomly coupled ferromagnet

Journal of Physics A: Mathematical and General, 1999

We show using extensive simulation results and physical arguments that an Ising system on a two dimensional square lattice, having interactions of random sign between first neighbors and ferromagnetic interactions between second neighbors, presents a phase transition at a non-zero temperature. *

On the Phase Diagram of the Random Field Ising Model on the Bethe Lattice

Journal of Statistical Physics, 2000

The ferromagnetic Ising model on the Bethe lattice of degree k is considered in the presence of a dichotomous external random field fx= +a and the temperature T>0. We give a description of a part of the phase diagram of this model in the T-a. plane, where we are able to construct limiting Gibbs states and ground states. By comparison with the model with a constant external field we show that for all realizations {={£x= ±a} of the external random field: (i) the Gibbs state is unique for T> Tc ( k > 2 and any a) or for a> 3 (k = 2 and any T); (ii) the +-phases coexist in the domain {T< T c , a . < H F ( T ) } , where Tc is the critical temperature and HF(T) is the critical external field in the ferromagnetic Ising model on the Bethe lattice with a constant external field. Then we prove that for almost all £,: (iii) the +-phases coexist in a larger domain { T< T c , a < H F ( T ) +e(T)}, where £(T)>0; and (iv) the Gibbs state is unique for 3 > a > 2 at any T. We show that the residual entropy at T-0 is positive for 3 > a > 2, and we give a constructive description of ground states, by so-called dipole configurations.

Phase diagram of the random field Ising model on the Bethe lattice

2001

The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the ferromagnetic and paramagnetic regime. Refining arguments of Bleher, Ruiz and Zagrebnov [J. Stat. Phys. 93, 33 (1998)] an exact upper bound for the existence of a unique paramagnetic phase is found which considerably improves the earlier results. Several numerical estimates of transition lines between a ferromagnetic and a paramagnetic regime are presented. The obtained results do not coincide with a lower bound for the onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If the latter one proves correct this would hint to a region of coexistence of stable ferromagnetic phases and a stable paramagnetic phase.

The Effect of a Random Crystal-Field on the Mixed Ising Spins (1/2, 3/2)

Acta Physica Polonica A, 2011

We study the magnetic properties of a mixed Ising ferrimagnetic system, in which the two interacting sublattices have spins σ, (± 1 2) and spins S, (± 3 2 , ± 1 2) in the presence of a random crystal field, with the mean field approach. The results obtained, using mean field approach and Monte Carlo simulation, show the appearance of a new ferrimagnetic phase, namely the partly ferrimagnetic phase (m σ = −1 2 , m S = +1). Consequently, three topologically different types of phase diagrams have been given by mean field approach. The effect of increasing the exchange interaction parameter J, at very low temperature is also investigated.

Analysis of a long-range random field quantum antiferromagnetic Ising model

The European Physical Journal B, 2006

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions and random fields on each site following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.

Theory of the Random Field Ising Model

Series on Directions in Condensed Matter Physics, 1997

A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

Self-averaging in the random two-dimensional Ising ferromagnet

Physical Review E

We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the probability distribution function of the critical internal energy and for the specific heat fluctuations. It is shown that the disorder distribution of internal energies is Gaussian, and the typical sample-to-sample fluctuations as well as the average value scale with the system size L like ∼ L ln ln(L). In contrast, the specific heat is shown to be self-averaging with a distribution function that tends to a δ-peak in the thermodynamic limit L → ∞. While previously a lack of self-averaging was found for the free energy, we here obtain results for quantities that are directly measurable in simulations, and implications for measurements in the actual lattice system are discussed.