# The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Exact Theory and Experimental Results

@article{Curely2019TheTI, title={The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Exact Theory and Experimental Results}, author={Jacques Cur'ely}, journal={arXiv: Statistical Mechanics}, year={2019} }

We rigorously examine 2d-infinite square lattices composed of classical spins isotropically coupled between first-nearest neighbors. Each local exchange Hamiltonian is expanded on the basis of its eigenfunctions played by spherical harmonics Yinf{l,m}. The corresponding eigenvalues are modified Bessel functions of the first kind. In the thermodynamic limit a numerical study allows one to select the higher-degree term of the characteristic polynomial associated with the zero-field partition…

## One Citation

### The Two-Dimensional Infinite Heisenberg Classical Square Lattice: Zero-Field Partition Function and Correlation Length

- PhysicsAmerican Journal of Theoretical and Applied Statistics
- 2021

We rigorously examine 2d-square lattices composed of classical spins isotropically coupled between first-nearest neighbours. A general expression of the characteristic polynomial associated with the…

## References

SHOWING 1-10 OF 54 REFERENCES

### Thermodynamics of the 2D-Heisenberg classical square lattice:: Zero-field partition function

- Mathematics
- 1998

### Zero-field Partition Function and Free Energy Density of the Two-Dimensional Heisenberg Classical Square Lattice

- Physics
- 2017

We rigorously examine 2d square lattices composed of Ninf{S} classical spins isotropically coupled. If Hsup{ex},inf{i,j} is the local exchange Hamiltonian each operator exp(-beta.Hsup{ex},inf{i,j})…

### The spin- 1/2 Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides

- Physics
- 1991

The spin-1/2 antiferromagnetic Heisenberg model on a square lattice is used to describe the dynamics of the spin degrees of freedom of undoped copper oxides. Even though the model lacks an exact…

### Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet

- PhysicsPhysical review. B, Condensed matter
- 1990

A neutron scattering study of the instantaneous spin correlations in the two-dimensional spin S=5/2 square-lattice Heisenberg antiferromagnet Rb2MnF4 finds that the data are outside of the regime corresponding to renormalized classical behavior of the quantum non-linear model.

### Vortex-liquid-vortex-crystal transition in type-II superconductors.

- PhysicsPhysical review. B, Condensed matter
- 1996

A functional renormalization group (FRG) study of a Landau-Ginzburg model of type-II superconductors in an external magnetic field in anExternal magnetic field is presented, both for a pure system and also in the presence of quenched random impurities.

### Critical fluctuations and disorder at the vortex liquid to crystal transition in type-II superconductors.

- PhysicsPhysical review letters
- 1995

We present a functional renormalization group (FRG) analysis of a Landau-Ginzburg model of type-II superconductors (generalized to $n/2$ complex fields) in a magnetic field, both for a pure system,…