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AIP conference proceedings

Monte Carlo renormalization group studies of the Baxter-Wu model in the presence of an external magnetic field

Ioannis N. Velonakis

Published Jan 1, 2015• 0 citations
Publisher
DOI
10.1063/1.4912646

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We have used a Monte Carlo renormalization-group method to study the Baxter-Wu model with random, quenched, nonmagnetic site impurities. The results clearly show that the impurities change the critical exponents from the zero-impurity exact value of \ensuremath{\nu}=(2/3) to \ensuremath{\nu}=0.97\ifmmode\pm\else\textpm\fi{}0.04. The magnetic and crossover exponents do not change measurably with the addition of the impurities. We also find that the fixed point for the model with quenched impurities is further from the starting Hamiltonian than it was for the pure model.
The effectiveness of a Monte Carlo renormalization-group method is studied by applying it to the Baxter-Wu model (Ising spins on a triangular lattice with three-spin interactions). The calculations yield three relevant eigenvalues in good agreement with exact or conjectured results. We demonstrate that the method is capable of distinguishing between models expected to be in the same universality class, when one of them (four-state Potts) exhibits logarithmic corrections to the usual power-law singularities and the other (Baxter-Wu) does not.
The two-dimensional Baxter-Wu model with spin-1, in the presence of a crystal field, is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic susceptibility are measured. Single histogram techniques are used to get the results close to the phase transitions. The finite-size scaling procedure is employed in order to obtain the critical behavior. The simulations have shown that the critical exponents are different from the spin-1/2 case and are crystal field dependent.