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arXiv:cond-mat/9711182 · Journal of Physics A Mathematical and General

Boundary critical behaviour of two-dimensional random Ising models

Ferenc Iglói, Péter Lajkó, Walter Selke, F. Szalma

Published Mar 27, 1998• 8 citations
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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, , of the correlation length, , and of the critical surface correlations, , are analysed.

DOI
10.1088/0305-4470/31/12/006

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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, , of the correlation length, , and of the critical surface correlations, , are analysed.
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.
\n \nUsing extensive Monte Carlo simulations, transfer matrix techniques \nand\nconformal invariance, ferromagnetic random\nq−q-q−state Potts models for 3leqle83\\le q\\le 83leqle8 are studied in the vicinity \nof the \ncritical temperature.\nIn particular the surface and bulk magnetization exponents beta1\\beta_1beta1​ \nand \nβ are found\nmonotonically increasing with q. At the critical temperature, \ndifferent \nmoments (n)\nof the magnetization profiles are calculated which are all found \nto accurately follow predictions of \nconformal invariance. The critical correlation functions \nshow multifractal behaviour, the decay exponents of the different \nmoments\nboth in the volume and at the surface, are n−n-n−dependent.\n \n\n