We formulate the spectral-density method in classical statistical mechanics in strict analogy with the known quantum version, and we apply it to the classical Heisenberg ferromagnetic model in an external field. A new formula for the magnetization in the classical formulation of spin-vector Green functions is derived for arbitrary spatial dimensionality. Furthermore, the static properties of the one- and three-dimensional cases are considered in detail. We obtain accurate results over a wide range of temperatures with the external field for the one-dimensional model and without field for the three-dimensional model. In the first case very good agreement with the exact numerical transfer-matrix data is also found in the region of higher temperature where the interacting-boson approach fails. In particular the zero-field susceptibility results are found to be consistent with the exact results obtained by Fisher.We formulate the spectral-density method in classical statistical mechanics in strict analogy with the known quantum version, and we apply it to the classical Heisenberg ferromagnetic model in an external field. A new formula for the magnetization in the classical formulation of spin-vector Green functions is derived for arbitrary spatial dimensionality. Furthermore, the static properties of the one- and three-dimensional cases are considered in detail. We obtain accurate results over a wide range of temperatures with the external field for the one-dimensional model and without field for the three-dimensional model. In the first case very good agreement with the exact numerical transfer-matrix data is also found in the region of higher temperature where the interacting-boson approach fails. In particular the zero-field susceptibility results are found to be consistent with the exact results obtained by Fisher.

Physical review. B, Condensed matterSep 1, 198424 citations

Low-temperature critical phenomena in the spin-1/2 planar ferromagnet

Dalcio Kisling Dacol

Journal of Low Temperature PhysicsNov 1, 198021 citations

Low-temperature critical properties and crossovers of a spin- 12 planar ferromagnet in 4−ε dimensions

Maria Teresa Mercaldo, Alvaro Caramico D’Auria, L. De Cesare +1 more

The low-temperature critical properties and crossovers of a spin- $\frac{1}{2}$ planar ferromagnet in a longitudinal magnetic field are explored in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions in terms of an anisotropic bosonic action, suitable to describe the spin model in the low-temperature regime. This is performed adopting a procedure, which combines a preliminary averaging over dynamic degrees of freedom and a next static Wilson renormalization group transformation. We work to one-loop level to obtain results which are exact to first order in $\ensuremath{\epsilon}$ and believed to be qualitatively correct for $2<d<4$ . Within this static framework, we get the phase boundary, ending in a quantum critical point, and the general expressions for the correlation length and susceptibility as functions of the temperature and the applied magnetic field within the disordered phase. With these basic ingredients, the critical properties and a rich crossover scenario in the influence domain of the quantum critical point are derived in a simple and transparent way. Remarkably, one can speculate that the crossovers, found to occur decreasing the temperature with the magnetic field fixed at its quantum critical point value, might be actually observable in complex magnetic compounds, as suggested by recent experiments.The low-temperature critical properties and crossovers of a spin-$\frac{1}{2}$ planar ferromagnet in a longitudinal magnetic field are explored in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions in terms of an anisotropic bosonic action, suitable to describe the spin model in the low-temperature regime. This is performed adopting a procedure, which combines a preliminary averaging over dynamic degrees of freedom and a next static Wilson renormalization group transformation. We work to one-loop level to obtain results which are exact to first order in $\ensuremath{\epsilon}$ and believed to be qualitatively correct for $2<d<4$. Within this static framework, we get the phase boundary, ending in a quantum critical point, and the general expressions for the correlation length and susceptibility as functions of the temperature and the applied magnetic field within the disordered phase. With these basic ingredients, the critical properties and a rich crossover scenario in the influence domain of the quantum critical point are derived in a simple and transparent way. Remarkably, one can speculate that the crossovers, found to occur decreasing the temperature with the magnetic field fixed at its quantum critical point value, might be actually observable in complex magnetic compounds, as suggested by recent experiments.

Physical Review BMay 20, 200814 citations

Critical behavior of the susceptibility in a two-dimensional ferromagnet

M. Aïn, J. Hammann

AIP conference proceedingsJan 1, 19753 citations

The low-temperature critical properties and crossovers of a spin-

\frac{1}{2}

planar ferromagnet in a longitudinal magnetic field are explored in $4\ensuremath{-}\ensuremath{\epsilon}$ dimensions in terms of an anisotropic bosonic action, suitable to describe the spin model in the low-temperature regime. This is performed adopting a procedure, which combines a preliminary averaging over dynamic degrees of freedom and a next static Wilson renormalization group transformation. We work to one-loop level to obtain results which are exact to first order in $\ensuremath{\epsilon}$ and believed to be qualitatively correct for

2<d<4

. Within this static framework, we get the phase boundary, ending in a quantum critical point, and the general expressions for the correlation length and susceptibility as functions of the temperature and the applied magnetic field within the disordered phase. With these basic ingredients, the critical properties and a rich crossover scenario in the influence domain of the quantum critical point are derived in a simple and transparent way. Remarkably, one can speculate that the crossovers, found to occur decreasing the temperature with the magnetic field fixed at its quantum critical point value, might be actually observable in complex magnetic compounds, as suggested by recent experiments.