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 = 1/2 J(1)-J(2) Heisenberg model on the 2D square lattice. We calculate the temperature dependence of the spin-spin correlation functions c(r) = <(S0Srz)-S-z >, the gaps in the spin excitation spectrum, the energy E and the heat capacity C-V for the whole J(1)-J(2)-circle, i.e. for arbitrary phi, J(1) = cos(phi), J(2) = sin(phi). Due to low dimension there is no long-range order at T not equal 0, but the short-range holds the memory of the parent zero-temperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E(phi) and C-V(phi) demonstrate extrema "above" the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of c(r) (phi) lines have several nodes leading to nonmonotonic c(r) (T) dependence. For any fixed phi the heat capacity C-V(T) always has maximum, tending to zero at T -> 0, in the narrow vicinity of phi = 155 degrees it exhibits an additional frustration-induced low-temperature maximum. We have also found the nonmonotonic behaviour of the spin gaps at phi = 270 degrees +/- 0 and exponentially small antiferromagnetic gap up to (T less than or similar to 0.5) for phi greater than or similar to 270 degrees. (C) 2016 Elsevier B.V. All rights reserved.