Thermodynamic properties of the 2D frustrated Heisenberg model for the entire J1-J2 circle

Using the spherically symmetric self-consistent Green's function method, we consider thermodynamic properties of the S=1/2J1-J2 Heisenberg model on the 2D square lattice. We calculate the temperature dependence of the spin-spin correlation functions cr=〈S0zSrz〉, the gaps in the spin excitation spectrum, the energy E and the heat capacity CV for the whole J1-J2-circle, i.e. for arbitrary φ, J1=cos(φ), J2=sin(φ). Due to low dimension there is no long-range order at T≠0, but the short-range holds the memory of the parent zero-temperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E(φ) and CV(φ) demonstrate extrema “above” the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of cr(φ) lines have several nodes leading to nonmonotonic cr(T) dependence. For any fixed φ the heat capacity CV(T) always has maximum, tending to zero at T→0, in the narrow vicinity of φ=155° it exhibits an additional frustration-induced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at φ=270°±0 and exponentially small antiferromagnetic gap up to (T≲0.5) for φ≳270°.