Boundary critical behaviour of two-dimensional random Ising models

TL;DR

This paper investigates the boundary critical behavior of two-dimensional random Ising models with mixed couplings, using Monte Carlo simulations and transformations to analyze surface and bulk critical exponents near phase transition.

Contribution

It provides new insights into how randomness affects surface and bulk critical exponents in 2D Ising models at phase transition.

Findings

Surface magnetization exponent beta_1 determined

Correlation length exponent nu measured

Surface correlation exponent eta_parallel analyzed

Abstract

Using Monte Carlo techniques and a star-triangle transformation, Ising models with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on a square lattice with a (1,1) surface are studied near the phase transition. Both surface and bulk critical properties are investigated. In particular, the critical exponents of the surface magnetization, 'beta_1', of the correlation length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are analysed.