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

The classical J₁-J₂ 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. 108, 045702 (2012), is that first-order phase transitions are ruled out in the region g=J₂/|J₁|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< such that it asymptotically becomes second order when g. We also find strong evidence that the phase boundary is first order in the region 0. 5<g0. 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 g0. 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.