Anisotropic deformation of the 6-state clock model: Tricritical-point classification

Abstract

The two-dimensional $q$-state clock models exhibit the Berezinskii-Kosterlitz-Thouless (BKT) transition for $q\ge 5$ since they are a subset of the isotropic XY model. We examine the $6$-state clock model with an anisotropic deformation. Selecting the $6$-state Potts model as a source of the deformation, the model naturally violates the discrete rotational symmetry of the clock model. We introduce the anisotropic deformation parameter $\alpha$ in the clock model interpolating the clock ($\alpha =1$) and the Potts ($\alpha =0$) models. We employ the corner transfer matrix renormalization group method to analyze the phase transitions on the square lattice in the thermodynamic limit. Three different phases and phase transitions are identified. The phase diagram is constructed, and we determine a tricritical point at ${\alpha }_{\mathrm{c}}=0.21405(4)$ and $T_{\mathrm{c}}=0.834017(5)$. Analyzing the latent heat and the entanglement entropy in the vicinity of the $T_{\mathrm{c}}({\alpha }_{\mathrm{c}})$, we observe a single discontinuous phase transition and two BKT phase transitions meeting in the tricritical point. The tricritical point exhibits a phase transition of the second order with the critical exponents $\beta \approx 1/10$ and $\delta \approx 14$. We conjecture that an infinitesimal surrounding of the tricritical point consists of the three fundamental phase transitions, in which the first and the BKT orders gradually weaken into the second-order tricritical point.

References in corpus (18)

• Corner Transfer Matrix Renormalization Group Method
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Density Matrix Renormalization Group Method for 2D Classical Models
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Quantum Engineering of Spin and Anisotropy in Magnetic Molecular Junctions
• Finite-size scaling method for the Berezinskii-Kosterlitz-Thouless transition
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Applications of neural networks to the studies of phase transitions of two-dimensional Potts models
• The Blume-Capel model for spins S=1 and 3/2 in dimensions d=2 and 3
• Odd q-State Clock Spin-Glass Models in Three Dimensions, Asymmetric Phase Diagrams, and Multiple Algebraically Ordered Phases
• Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model
• A Neural Networks study of the phase transitions of Potts model
• Tricritical point of J1-J2 Ising model on hyperbolic lattice
• Neural Network flows of low q-state Potts and clock Models
• Phase transition of the six-state clock model observed from the entanglement entropy
• Thermodynamic model of social influence on two-dimensional square lattice: Case for two features
• Entanglement-entropy study of phase transitions in six-state clock model
• Anisotropic magnetic interactions and spin dynamics in the spin-chain compound Cu(py)${}_2$Br${}_2$: An experimental and theoretical study

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