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.

15 pages, 19 figures

References in corpus (13)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The iTEBD algorithm beyond unitary evolution
• Scaling of entanglement support for Matrix Product States
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• First order phase transition in the anisotropic quantum orbital compass model
• Deconfined quantum critical point in one dimension
• Transfer Matrices and Excitations with Matrix Product States
• Phase diagram of the Ising square lattice with competing interactions
• Location of the Potts-critical end point in the frustrated Ising model on the square lattice
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Phase transitions in a frustrated Ising antiferromagnet on a square lattice
• Monte Carlo studies of the Ising square lattice with competing interactions
• Metastable states in the J1-J2 Ising model

Cited by in corpus (6)

• Phase determination with and without deep learning
• Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping
• Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model
• Emergent Intermediate Phase in the $J_1$-$J_2$ XY model from Tensor Network Approaches
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions
• Nonequilibrium tricritical behaviour in anisotropic XY ferromagnet driven by elliptically polarised propagating magnetic field wave