Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model

Abstract

The classical $J_1$-$J_2$ Ising model on the square lattice is a minimal model of frustrated magnetism whose phase boundaries have remained under scrutiny for decades. Signs of first-order phase transitions have appeared in some studies, but strong evidence remains lacking. The current consensus, based upon the numerical data and theoretical arguments in [S. Jin et al., Phys. Rev. Lett. \textbf{108}, 045702 (2012)], is that first-order phase transitions are ruled out in the region $g=J_2/|J_1|\gtrsim 0.67$. We point out a loophole in the basis for this consensus, and we find strong evidence that the phase boundary is instead weak first-order at $0.67\lesssim g<\infty$ such that it asymptotically becomes second-order when $g\to \infty$. We also find strong evidence that the phase boundary is first-order in the region $0.5<g\lesssim 0.67$. We establish these results with adiabatic evolution of matrix product states directly in the thermodynamic limit, and with the theory of finite entanglement scaling. We also find suggestive evidence that when $g\to 0.5^{+}$, the phase boundary becomes of an anomalous first-order type wherein the correlation length is very large in one of the coexisting phases but very small in the other.

arXiv comment15 pages, 19 figures

References in corpus (35)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Tensor networks for complex quantum systems
• The iTEBD algorithm beyond unitary evolution
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Renormalization and tensor product states in spin chains and lattices
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Scaling of entanglement support for Matrix Product States
• Ashkin-Teller criticality and pseudo first-order behavior in a frustrated Ising model on the square lattice
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Phase transitions in the frustrated Ising model on the square lattice
• First order phase transition in the anisotropic quantum orbital compass model
• Finite correlation length scaling with infinite projected entangled-pair states
• Numerical Renormalization Group at Criticality
• Deconfined quantum critical point in one dimension
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Transfer Matrices and Excitations with Matrix Product States
• Phase diagram of the Ising square lattice with competing interactions
• Monte Carlo studies of the square Ising model with next-nearest-neighbor interactions
• Location of the Potts-critical end point in the frustrated Ising model on the square lattice
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Detecting signals of weakly first-order phase transitions in two-dimensional Potts models
• Analysis of the phase transition for the Ising model on the frustrated square lattice
• Dynamic Approach to Weak First Order Phase Transitions
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Doubling of Entanglement Spectrum in Tensor Renormalization Group
• Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Phase transitions in a frustrated Ising antiferromagnet on a square lattice
• Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model
• Monte Carlo studies of the Ising square lattice with competing interactions
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• One-dimensional model for deconfined criticality with ${\mathbb{Z}}_3\times {\mathbb{Z}}_3$ symmetry
• Metastable states in the J1-J2 Ising model
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• A direct calculation of critical exponents of two-dimensional anisotropic Ising model

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