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Journal of Physics A Mathematical and General

Critical behaviour of two Ising models with near-neighbour exclusion

Ferenc Iglói, Jouke R. Heringa, M M F Philippens, A. Hoogland, Henk W. J. Blöte

Published Dec 7, 1992• 4 citations
Publisher

Abstract

The authors have performed extensive Monte Carlo simulations of two-dimensional layered Ising lattice gases with (m-1)-neighbour exclusion in the x direction and pair attraction in the y direction. They studied the specific heat of the models in systems with different rectangular shapes and the spin-spin correlation function in the x direction near to the critical point. For the m=3 model both the thermal and magnetic exponents were estimated to be close to the known values of the three-state Potts model. Estimates for the critical exponents of the m=4 model are consistent with a commensurate-incommensurate transition; however they find no independent evidence for the existence of a floating phase.

DOI
10.1088/0305-4470/25/23/019

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The authors have performed extensive Monte Carlo simulations of two-dimensional layered Ising lattice gases with (m-1)-neighbour exclusion in the x direction and pair attraction in the y direction. They studied the specific heat of the models in systems with different rectangular shapes and the spin-spin correlation function in the x direction near to the critical point. For the m=3 model both the thermal and magnetic exponents were estimated to be close to the known values of the three-state Potts model. Estimates for the critical exponents of the m=4 model are consistent with a commensurate-incommensurate transition; however they find no independent evidence for the existence of a floating phase.
The two-dimensional random bond Ising model with two distinct ferromagnetic nearest-neighbour couplings, J and J ', distributed randomly over the lattice with concentration 1/2 is studied for various ratios J '/ J at criticality. The critical temperature is exactly known from self-duality. The size-dependent specific heat shows a crossover from the perfect Ising to the randomness-dominated critical behaviour of doubly logarithmic form. In the latter region, our estimates for the critical exponents of the size-dependent magnetization and susceptibility are in very good agreement with analytic results suggesting β/ν = 1/8 and γ/ν = 7/4.
The phase transition of the three-dimensional random field Ising model with a discrete (+or-h) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the magnetization appears to be discontinuous, the specific heat appears to saturate, indicating no latent heat. Sample-to-sample fluctuations of the susceptibility are consistent with the droplet picture for the transition.
The critical relaxation of the magnetization in a two-dimensional Ising model with quenched random non-magnetic impurities has been studied by numerical simulation. A squared lattice of size 400 2 with spin concentrations p=1.0; 0.95, 0,9, 0.85, 0.8, 0.75 and 0.7 was considered. The dynamical critical exponent z was determined by the Monte Carlo method combined with the dynamical renormalization group method. The following values were received for z(p): z(1)=2.24+or-0.07, z(0.95)=2.24+or-0.06, z(0.9)=2.24+or-0.06, z(0.85)=2.38+or-0.05, z(0.8)=2.51+or-0.06, z(0.75)=2.66+or-0.07 and z(0.7)=2.88+or-0.06. A singular dynamic scaling behaviour with z=A' mod ln(p-p c ) mod +B' was found for systems with spin concentrations p<or=0.85 near the percolation threshold p c , where A'=0.56+or-0.07 and B'=1.62+or-0.07 are temperature-independent constants.