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Physica A Statistical Mechanics and its Applications

Shift exponent and breakdown of universality for the two-layer Ising model on a square lattice

Tsuyoshi Horiguchi, Norihiro Tsushima

Published Apr 1, 1997• 21 citations
Publisher
DOI
10.1016/s0378-4371(96)00445-1

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Journal of Physics Condensed Matter•Aug 6, 2009•8 citations
The critical behaviour of the square-lattice Ising model, with nearest and next-nearest neighbour interactions of either sign, has been investigated by means of high-temperature series. lhe location of the critical lines in the coupling constant plane has been accurately determined. Along the critical line which corresponds to transitions to the layered or superantiferromagnetic state a breakdown of universality is observed and explicit numerical estimates obtained for the exponent of the ordering susceptibility.
Layered square-lattice ferromagnetic Ising models (∞×∞× n lattices) are studied by the Monte Carlo simulation with the periodic boundary condition( n = 3 ∼8) and with the free boundary condition ( n = 4 ∼14) in the n -direction. The results show the dimensionality crossover from the square-lattice Ising model to the simple-cubic Ising model. The shift exponent λ shows the size dependent behavior contrary to the previous results, and goes to about λ∼1.60 in the limit, n → ∞, for both boundary conditions, which is consistent with λ= 1/ ν 3d .
The site-diluted Ising ferromagnet is investigated on a square lattice, within short-time-dynamics numerical simulations, for different site concentrations. The dynamical exponents θ and z are obtained and it is shown that these exponents do depend strongly on the disorder, exhibiting a clear breakdown of universality, characterized by relative variations of nearly 100% in the range of site concentrations investigated. In what concerns the static exponents β and ν, universality is preserved within the error bars.