Spin-wave theory at constant order parameter

Abstract

We derive the low-temperature properties of spin-S quantum Heisenberg magnets from the Gibbs free energy G(M ) for fixed order parameter M . Assuming that the low-lying elementary excitations of the system are renormalized spin waves, we show that a straightforward 1/S expansion of G(M ) yields qualitatively correct results for the low-temperature thermodynamics, even in the absence of long-range magnetic order. We explicitly calculate the two-loop correction to the susceptibility of the ferromagnetic Heisenberg chain and show that it quantitatively modifies the mean-field result.

Magnetic properties of a metal-organic antiferromagnet on a distorted honeycomb lattice

“…For a square lattice this yields withJ 0 = 4J and 9) which is identical to Takahashi's result (see Eq. (27a) in Ref.…”

“…In fact, the field h s (h) is nothing but the Lagrange multiplier introduced in Takahashi's modified spin-wave theory. 9,17 It is well known that the internal field is related to a finite correlation length ξ, as we will further discuss in Sec. IV C. Numerically, we calculate the uniform magnetization m(h, T ) at finite temperature T by adjusting h s for fixed external field h such that the condition n = 0 is fulfilled in Eqs.…”

Exact renormalization group for quantum spin systems

“…However, in the absence of long-range magnetic order the 1/Sexpansion is not applicable. Several alternative methods have been developed to study quantum magnets without magnetic order, such as modifications of spin-wave theory where the vanishing magnetization is externally enforced [10,11], Schwinger-boson mean-field theory [1,12], and mean-field theories relying on the representation of the spin operators in terms of Abrikosov pseudofermions [13,14] or Majorana fermions [15][16][17][18].…”

“…The exact FRG flow of the generating functional of the irreducible spin vertices is then given by Eq. (11). By expanding both sides in powers of the components of the fluctuating magnetization M α i (τ ), we obtain the usual hierarchy of coupled FRG flow equations [23].…”

Ferromagnetism in one-dimensional metals: Breakdown of the Hartree-Fock approximation and possible first-order phase transition

“…To study spontaneous symmetry breaking, it is more convenient to work with the corresponding Gibbs potential 7,8,9 …”