The tensor renormalization group study of the general spin-S Blume-Capel model

Abstract

We focus on the special situation of $D=2J$ of the general spin-S Blume-Capel model on the square lattice. Under the infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are discussed by the newly developed tensor renormalization group method. For the case of the integer spin-S, the system will undergo $S$ first-order phase transitions with the successive symmetry breaking with the magnetization $M=S,S-1,...0$. For the half-integer spin-S, there are similar $S-1/2$ first order phase transition with $M=S,S-1,...1/2$ stepwise structure, in addition, there is a continuous phase transition due to the spin-flip $Z_2$ symmetry breaking. In the low temperature regions, all first-order phase transitions are accompanied by the successive disappearance of the optional spin-component pairs($s,-s$), furthermore, the critical temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of the magnetic field, the visualization parameter characterizing the intrinsic degeneracy of the different phases clearly demonstrates the phase transition process.

6 pages, 7 figures

References in corpus (12)

• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Second Renormalization of Tensor-Network States
• Renormalization of tensor-network states
• Multicritical Points and Crossover Mediating the Strong Violation of Universality: Wang-Landau Determinations in the Random-Bond $d=2$ Blume-Capel model
• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• First-order phase transition and tricritical scaling behavior of the Blume-Capel model: a Wang-Landau sampling approach
• Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice
• Rigorous Solution of the Spin-1 Quantum Ising Model with Single-ion Anisotropy
• The fine structure of the entanglement entropy in the classical XY model
• Exact solutions of a class of S=1 quantum Ising spin models

Cited by in corpus (3)

• The Blume-Capel model for spins S=1 and 3/2 in dimensions d=2 and 3
• First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows