Ising transition in the two-dimensional quantum J₁-J₂ Heisenberg model

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We study the thermodynamics of the spin-S two-dimensional quantum Heisenberg antiferromagnet on the square lattice with nearest (J₁) and next-nearest (J₂) neighbor couplings in its collinear phase (J₂/J₁>0.5), using the pure-quantum self-consistent harmonic approximation. Our results show the persistence of a finite-temperature Ising phase transition for every value of the spin, provided that the ratio J₂/J₁ is greater than a critical value corresponding to the onset of collinear long-range order at zero temperature. We also calculate the spin- and temperature-dependence of the collinear susceptibility and correlation length, and we discuss our results in light of the experiments on Li₂VOSiO₄ and related compounds.