A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S -matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z = 2 where the S -matrix equals − 1. For fermions we find T c / T F ≈0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose–Einstein condensation. This bosonic critical point occurs at n λ T 3 ≈1.3, where n is the density and λ T the thermal wavelength, which is lower than the ideal gas value of ζ(3/2) = 2.61.A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S -matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z = 2 where the S -matrix equals − 1. For fermions we find T c / T F ≈0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose–Einstein condensation. This bosonic critical point occurs at n λ T 3 ≈1.3, where n is the density and λ T the thermal wavelength, which is lower than the ideal gas value of ζ(3/2) = 2.61.

arXiv:1004.5390Journal of Statistical Mechanics Theory and ExperimentJul 1, 20109 citations

Renormalization-group methods for critical dynamics: II. Detailed analysis of the relaxational models

Bertrand I. Halperin, Pierre C. Hohenberg, Shang-keng Ma

The relaxational models introduced in a previous treatment of critical dynamics are studied in detail using renormalization-group methods. The earlier results are justified by an analysis to all order in $\ensuremath{\epsilon}=4\ensuremath{-}d$, where $d$ is the dimensionality. The diagrammatic formalism of the full dynamic renormalization group is presented, and applied to the earlier models. A generalization of Wilson's Feynman-graph expansion method is used to calculate the exponents to second order in $\ensuremath{\epsilon}$. In model $C$ , where a nonconserved order parameter is coupled to a conserved energy field, ambiguities were found in the earlier recursion-relation treatment for $2<n<4$ , $d\ensuremath{\approx}4$ ( $n$ is the number of components of the order parameter). These ambiguities are discussed in the present work, but are not fully resolved.The relaxational models introduced in a previous treatment of critical dynamics are studied in detail using renormalization-group methods. The earlier results are justified by an analysis to all order in $\ensuremath{\epsilon}=4\ensuremath{-}d$, where $d$ is the dimensionality. The diagrammatic formalism of the full dynamic renormalization group is presented, and applied to the earlier models. A generalization of Wilson's Feynman-graph expansion method is used to calculate the exponents to second order in $\ensuremath{\epsilon}$. In model $C$, where a nonconserved order parameter is coupled to a conserved energy field, ambiguities were found in the earlier recursion-relation treatment for $2<n<4$, $d\ensuremath{\approx}4$ ($n$ is the number of components of the order parameter). These ambiguities are discussed in the present work, but are not fully resolved.

Physical review. B, Solid stateMay 1, 197675 citations

d

is the dimensionality. The diagrammatic formalism of the full dynamic renormalization group is presented, and applied to the earlier models. A generalization of Wilson's Feynman-graph expansion method is used to calculate the exponents to second order in $\ensuremath{\epsilon}$. In model

C

, where a nonconserved order parameter is coupled to a conserved energy field, ambiguities were found in the earlier recursion-relation treatment for

2<n<4

, $d\ensuremath{\approx}4$ (

n

is the number of components of the order parameter). These ambiguities are discussed in the present work, but are not fully resolved.