Partial long-range order in antiferromagnetic Potts models

Abstract

The Potts model plays an essential role in classical statistical mechanics, illustrating many fundamental phenomena. One example is the existence of partially long-range-ordered states, in which some degrees of freedom remain disordered. This situation may arise from frustration of the interactions, but also from an irregular but unfrustrated lattice structure. We study partial long-range order in a range of antiferromagnetic $q$-state Potts models on different two-dimensional lattices and for all relevant values of $q$. We exploit the power of tensor-based numerical methods to evaluate the partition function of these models and hence to extract the key thermodynamic properties -- entropy, specific heat, magnetization, and susceptibility -- giving deep insight into the phase transitions and ordered states of each system. Our calculations reveal a range of phenomena related to partial ordering, including different types of entropy-driven phase transition, the role of lattice irregularity, very large values of the critical $q_c$, and double phase transitions.

23 pages, 27 figures

References in corpus (37)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement renormalization
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Coarse-graining renormalization by higher-order singular value decomposition
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Second Renormalization of Tensor-Network States
• Fermionic Projected Entangled Pair States
• Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
• Renormalization of tensor-network states
• Variational quantum Monte Carlo simulations with tensor-network states
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systems
• Tensor renormalization group study of classical XY model on the square lattice
• Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
• The 3-State Square-Lattice Potts Antiferromagnet at Zero Temperature
• Numerical study of the hard-core Bose-Hubbard Model on an Infinite Square Lattice
• Partial order and finite-temperature phase transitions in Potts models on irregular lattices
• Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice
• Phase Transition Properties of 3D Potts Models
• Efficient evaluation of partition functions of frustrated and inhomogeneous spin systems
• Transfer matrix computation of critical polynomials for two-dimensional Potts models
• Partial Disorder in the Periodic Anderson Model on a Triangular Lattice
• Finite-temperature phase transition in a class of 4-state Potts antiferromagnets
• Phase transition in the 3-state Potts antiferromagnet on the diced lattice
• Plaquette Renormalization Scheme for Tensor Network States
• On the universality of compact polymers
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
• The 3-State Potts Antiferromagnet on the Hexagonal Lattice
• Partial order in Potts models on the generalized decorated square lattice
• The 3-edge-colouring problem on the 4-8 and 3-12 lattices
• Carrier doping to a partially disordered state in the periodic Anderson model on a triangular lattice
• Partial order in a frustrated Potts model

Cited by in corpus (7)

• Lecture Notes of Tensor Network Contractions
• Ising antiferromagnet on the 2-uniform lattices
• Frustrations on decorated planar lattices in Ising model
• A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model
• Spontaneous magnetization of Kagome lattice in Ising model
• Three lectures on random proper colorings of ${\mathbb{Z}}^d$
• Frustrations on decorated triangular lattice in Ising model