Weak first-order phase transitions in the frustrated square lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> classical Ising model
Adil A. Gangat
Abstract
The classical ${J}_{1}\ensuremath{-}{J}_{2}$ 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. 108, 045702 (2012)], is that first-order phase transitions are ruled out in the region $g={J}_{2}/|{J}_{1}|\ensuremath{\gtrsim}0.67$. 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 $0.67\ensuremath{\lesssim}g<\ensuremath{\infty}$ such that it asymptotically becomes second order when $g\ensuremath{\rightarrow}\ensuremath{\infty}$. We also find strong evidence that the phase boundary is first order in the region $0.5<g\ensuremath{\lesssim}0.67$. 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 $g\ensuremath{\rightarrow}0.{5}^{+}$, 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.