Monte Carlo Renormalization Group Method to Study the First-Order Phase Transition in the Complex Ferromagnet

Anna Hazenfratz

Chin‐Kun Hu, Jau-Ann Chen

Qing-Kuan Meng, Dong-Tai Feng, Xu-Tuan Gao

An improved Monte Carlo renormalization group method is established. Based on a new model, as well as the generalized Glauber dynamics, the first-order phase transition is studied in the Erdös–Rényi network, which is used to represent the complex ferromagnet. Both static and dynamic critical exponents can be evaluated simultaneously, and the static critical exponents are evaluated to be independent of the dimension of the system. Thus by using the hyperscaling relation νd* = 2 − α, the effective dimension d* of complex networks can be found.

Qing-Kuan Meng, Dong-Tai Feng, Xu-Tuan Gao +1 more

At zero temperature, based on the Ising model, the phase transition in a two-dimensional square lattice is studied using the generalized zero-temperature Glauber dynamics. Using Monte Carlo (MC) renormalization group methods, the static critical exponents and the dynamic exponent are studied; the type of phase transition is found to be of the first order.

O. Idigoras, P. Vavassori, Andreas Berger

Shun Wang, Zhi-Yuan Xie, Jing Chen +2 more

We investigate the 2- and 3-state ferromagnetic Potts models on the simple cubic lattice using the tensor renormalization group method with higher-order singular value decomposition (HOTRG). HOTRG works in the thermodynamic limit, where we use the Z q symmetry of the model, combined with a new measure for detecting the transition, to improve the accuracy of the critical point for the 2-state model by two orders of magnitude, obtaining T c = 4.51152469(1). The 3-state model is far more complex, and we improve the overall understanding of this case by calculating its thermodynamic quantities with high accuracy. Our results verify that the first-order nature of the phase transition and the HOTRG transition temperature benchmarks the most recent Monte Carlo result.