Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully non-universal

Abstract

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the Corner Transfer Matrix Renormalization Group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on model's parameters agree with Baxter's exact solution and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents $\eta$ and $\delta$ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ${\eta }_{\mathrm{e}}$ and ${\delta }_{\mathrm{e}}$ which agree with our numerical data. These exponents depend on model's parameters which is an evidence for the full non-universality of the symmetric eight-vertex model in the original electric formulation.

arXiv comment13 pages, 19 figures. arXiv admin note: text overlap with arXiv:1610.08657

References in corpus (26)

• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Quantum Inverse Scattering Method and Correlation Functions
• Corner Transfer Matrix Renormalization Group Method
• Unconventional critical behaviour in a quasi-two-dimensional organic conductor
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Interacting classical dimers on the square lattice
• Density Matrix Renormalization Group and Reaction-Diffusion Processes
• Lattice fermion models with supersymmetry
• Numerical Renormalization Group at Criticality
• The antiferromagnetic transition for the square-lattice Potts model
• Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain
• One-boundary Temperley-Lieb algebras in the XXZ and loop models
• Exact entanglement entropy of the XYZ model and its sine-Gordon limit
• Network Models of Quantum Percolation and Their Field-Theory Representations
• Bethe Ansatz for the Temperley-Lieb loop model with open boundaries
• Supersymmetry and Localization in the Quantum Hall Effect
• The eight-vertex model and lattice supersymmetry
• Scaling behavior of a square-lattice Ising model with competing interactions in a uniform field
• Critical exponents at the ferromagnetic transition in tetrakis(diethylamino)ethylene-C${}_{60}$ (TDAE-C${}_{60}$)
• A percolation model with continuously varying exponents
• Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices
• Low Temperature Static and Dynamic Behaviour of the Easy-Axis Heisenberg Antiferromagnet on the Kagome Lattice
• Reentrant disorder-disorder transitions in generalized multicomponent Widom-Rowlinson models
• Critical properties of the eight-vertex model in a field

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