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International Journal of Modern Physics C

MULTICANONICAL SIMULATION OF SPIN SYSTEMS WITH BOND RANDOMNESS

Fatih Yaşar

Published Jul 1, 2001• 0 citations
Publisher

Abstract

In order to test the multicanonical approach in simulations of the spin systems with quenched bond randomness, I simulated the q = 8 state Potts model in two dimensions with various degrees of randomness. It appears quite feasible to simulate spin systems with quenched bond randomness by multicanonical algorithm, but extra care is needed with increasing randomness.

DOI
10.1142/s0129183101001973

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In order to test the multicanonical approach in simulations of the spin systems with quenched bond randomness, I simulated the q = 8 state Potts model in two dimensions with various degrees of randomness. It appears quite feasible to simulate spin systems with quenched bond randomness by multicanonical algorithm, but extra care is needed with increasing randomness.
Monte Carlo simulations using the recently proposed Wang–Landau algorithm are performed to the q = 8 state Potts model in two dimension with various degrees of randomness. We systematically studied the effect of quenched bond randomness to system which has first-order phase transition. All simulations and measurements were done from pure case r = 1 to r = 0.4. Physical quantities such as energy density and ground-state entropy were evaluated at all temperatures. We have also obtained probability distributions of energy to monitor softening of transitions. It appears quite feasible to simulate spin systems with quenched bond randomness by Wang–Landau algorithm.
We have simulated, by using a cluster algorithm, the q=8q=8q=8 state Potts model in two dimensions with a varying amount of quenched bond randomness. We have shown that there exists a finite size-dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and that this threshold value becomes smaller as the system size increases.
The influence of uncorrelated, quenched disorder on the phase transition of two dimensional Potts models will be reviewed. After an introduction where the conditions of relevance of quenched randomness on phase transitions are exemplified by experimental measurements, the results of perturbative and numerical investigations in the case of the Potts model will be presented. The Potts model is of particular interest, since it can have in the pure case a second-order or a first-order transition, depending on the number of states per spin. In 2D, transfer matrix calculations and Monte Carlo simulations were used in order to check the validity of conformal invariance methods in disordered systems. These techniques were then used to investigate the universality class of the disordered Potts model, in both regimes of the pure model phase transitions. A test of replica symmetry became possible through a study of multiscaling properties and a detailed analysis of the probability distribution of the correlation functions was also made possible.