Study of the fully frustrated clock model using the Wang–Landau algorithm

Abstract

Monte Carlo simulations using the newly proposed Wang-Landau algorithm together with the broad histogram relation are performed to study the antiferromagnetic six-state clock model on the triangular lattice, which is fully frustrated. We confirm the existence of the magnetic ordering belonging to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral ordering which occurs at slightly higher temperature. We also observe the lower temperature phase transition of KT type due to the discrete symmetry of the clock model. By using finite-size scaling analysis, the higher KT temperature T2 and the chiral critical temperature Tc are respectively estimated as T2 = 0.5154(8) and Tc = 0.5194(4). The results are in favor of the double transition scenario. The lower KT temperature is estimated as T1 = 0.496(2). Two decay exponents of KT transitions corresponding to higher and lower temperatures are respectively estimated as η2 = 0.25(1) and η1 = 0.13(1), which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

Fast flat-histogram method for generalized spin models

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Search for the non-canonical Ising spin glass on rewired square lattices

“…Very recently we studied Heisenberg model on rewired square lattice and found no SG transition [14]. Due to the importance of discreteness in phase transition [15,16], here we study Ising model on rewired square lattices. The remaining part of the paper is organized as the following: We describe in Section II the model and method; discuss the result is in Section III.…”