# Interaction Corrections to Spin-Wave Theory in the Large-S Limit of the Quantum Heisenberg Ferromagnet

@article{Benedikter2016InteractionCT, title={Interaction Corrections to Spin-Wave Theory in the Large-S Limit of the Quantum Heisenberg Ferromagnet}, author={Niels Benedikter}, journal={Mathematical Physics, Analysis and Geometry}, year={2016}, volume={20}, pages={1-21} }

The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculate the first order interaction correction to the free energy, as an upper bound in the limit where the spin size S∞8$S \to \infty $ and ßS is fixed (ß being the inverse temperature). Our result is valid in two and three spatial dimensions. We extrapolate our result to compare with Dyson’s low-temperature expansion…

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## References

SHOWING 1-10 OF 30 REFERENCES

### The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

- Physics
- 2012

We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves…

### Spin waves in quantum ferromagnets

- Physics
- 1984

Low-temperature properties of Heisenberg quantum ferromagnets (“spin waves”) are derived within aconfiguration space formalism. Most of the work is done without explicitly assuming translational…

### Validity of the Spin-Wave Approximation for the Free Energy of the Heisenberg Ferromagnet

- Physics
- 2015

We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins S ≥ 1/2. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the…

### Theory of Spin-Wave Interactions in Ferro- and Antiferromagnetism

- Physics
- 1960

The spin-wave theory in an ideal Heisenberg model of a ferromagnet is studied using Holstein and Primakoff's method including the spin-wave interactions. Several earlier published results of the…

### On the spin wave problem in the Heisenberg model of Ferromagnetism

- Physics
- 1965

The interacting spin system of the Heisenberg model is brought into contact with a system of free Bose particles which are independent of the spins. The partition function of the combined system…

### Spontaneous magnetization of an ideal ferromagnet: Beyond Dyson's analysis

- Physics
- 2011

Using the low-energy effective field theory for magnons, we systematically evaluate the partition function of the O(3) ferromagnet up to three loops. Dyson, in his pioneering microscopic analysis of…

### General Theory of Spin-Wave Interactions

- Physics
- 1956

An ideal model of a ferromagnet is studied, consisting of a lattice of identical spins with cubic symmetry and with isotropic exchange coupling between nearest neighbors. The aim is to obtain a…

### Improved lower bound on the thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet

- Physics
- 1993

We introduce a new stochastic representation of the partition function of the spin 1/2 Heisenberg ferromagnet. We express some of the relevant thermodynamic quantities in terms of expectations of…

### Spontaneous magnetization of the O(3) ferromagnet at low temperatures

- Physics
- 2002

We investigate the low-temperature behavior of ferromagnets with a spontaneously broken symmetry $\mathrm{O}(3)\ensuremath{\rightarrow}\mathrm{O}(2).$ The analysis is performed within the perspective…

### Infrared bounds, phase transitions and continuous symmetry breaking

- Physics
- 1976

We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ)32 quantum field theories and classical, isotropic…