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

Abstract

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 = S z 0 S z r , 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 ϕ, J 1 = cos(ϕ), J 2 = 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 zerotemperature ordered phase (antiferromagnetic, stripe or ferromagnetic). E(ϕ) and C V (ϕ) demonstrate extrema "above" the long-range ordered phases and in the regions of rapid short-range rearranging. Tracts of c r (ϕ) lines have several nodes leading to nonmonotonic c r (T ) dependence. For any fixed ϕ the heat capacity C V (T ) always has maximum, tending to zero at T → 0, in the narrow vicinity of ϕ = 155 • it exhibits an additional frustrationinduced 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 • . PACS codes

Magnetic spiral order in the square-lattice spin system (CuBr)Sr2Nb3O10

“…( 6) fixes a vertex correction, introduced at the decoupling of many-particle Greens functions, see, e.g. [27,28] for details. Note also, eq.…”

Spectral characteristics of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field

“…(11,12) are close to Eqs. (6,7). But here the term with h and nondiagonal in 𝛼𝛽 indexes GF 𝐺 𝑦𝑥 k (𝜔) arises for the first time.…”

“…The consideration of a two dimensional quantum antiferromagnet (2D-AFM) is usually based on various versions of the spin- 1 2 Heisenberg square-lattice model. This model continues to be studied [1,2,3,4,5,6,7,8]. It is used to describe superconducting cuprates and related compounds, including recently synthesized molecular 2D AFM [9,10,11,12].…”

“…Our consideration is based on a spherically symmetric self-consistent approach (SSSA) [6,24,25,26,27]. Three degenerate branches of spin excitations are realized in the SSSA at h = 0.…”

“…The approach needs to consider the second step -the differentiation of the right side of (6). Taking into account that the commutator [[ ̂︀ 𝑆 𝛼 n ; Ĵ]; ĥ] = 0, we have the following exact expression for 𝐺 𝑧𝑧 k (𝜔):…”