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

The classical Jâ‚ − Jâ‚‚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. Jinet al.,Phys. Rev. Lett.108, 045702 (2012)], is that first-order phase transitions are ruled out in the regiong = Jâ‚‚/|Jâ‚| ≳ 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 at0.67 ≲ g < ∞such that it asymptotically becomes second order wheng → ∞. We also find strong evidence that the phase boundary is first order in the region0.5 < g ≲ 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 wheng → 0.5âº, 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. ; © 2024 American Physical Society. ; We acknowledge Anders Sandvik for drawing this problem to our attention and for discussions and feedback. We acknowledge Glen Evenbly for pointing out Ref.[47], for suggesting computation of pseudocritical point locations via fitting, and for technical help. We acknowledge Wangwei Lan for technical help and discussions. We also acknowledge discussions with Ying-Jer Kao, Ian McCulloch, Adam Iaizzi, André-Marie Tremblay, Thomas Baker, Ben Powell, Logan Wright, and Kai-Hsin Wu. This research was partly supported by the Australian Research Council Centre of Excellence for Engineered Quantum Systems (EQUS, CE170100009).