We study the crossover between two- and three-dimensional behaviors of the Villain form of the XY spin model on a three-dimensional lattice with anisotropic couplings ${\mathit{J}}_{1}$ = ${\mathit{J}}_{2}$ =J, ${\mathit{J}}_{3}$ =\ensuremath{\alpha}J (0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1). The \ensuremath{\alpha} dependence of various quantities is examined by means of duality transformations, Migdal renormalization group, and Monte Carlo simulations. For the specific heat, a crossover into the Kosterlitz-Thouless behavior takes place around \ensuremath{\alpha}\ensuremath{\simeq}0.2, which corresponds to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{cos}}$\ensuremath{\simeq}0.015 in the cosine form of the XY model. Some implications for models of high- ${\mathit{T}}_{\mathit{c}}$ superconductivity are discussed.We study the crossover between two- and three-dimensional behaviors of the Villain form of the XY spin model on a three-dimensional lattice with anisotropic couplings ${\mathit{J}}_{1}$=${\mathit{J}}_{2}$=J, ${\mathit{J}}_{3}$=\ensuremath{\alpha}J (0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1). The \ensuremath{\alpha} dependence of various quantities is examined by means of duality transformations, Migdal renormalization group, and Monte Carlo simulations. For the specific heat, a crossover into the Kosterlitz-Thouless behavior takes place around \ensuremath{\alpha}\ensuremath{\simeq}0.2, which corresponds to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{cos}}$\ensuremath{\simeq}0.015 in the cosine form of the XY model. Some implications for models of high-${\mathit{T}}_{\mathit{c}}$ superconductivity are discussed.

Physical review. B, Condensed matterDec 1, 199055 citations

Infinite set of crossover exponents of theXYmodel and f(α) approach

B. Fourcade, A.–M. S. Tremblay

For transitions described by the XY model, it has been shown that each Fourier component of the angular-structure factor is controlled by a different crossover exponent. Each crossover exponent is associated with a particular symmetry-breaking field. It is shown here that although, as for multifractals, the angular structure itself can be obtained from the crossover exponents, in contrast to multifractals, the asymptotic form of this angular-structure factor is described by the Legendre transform of the (analytically continued) infinite set of crossover exponents only in the special case of two dimensions.For transitions described by the XY model, it has been shown that each Fourier component of the angular-structure factor is controlled by a different crossover exponent. Each crossover exponent is associated with a particular symmetry-breaking field. It is shown here that although, as for multifractals, the angular structure itself can be obtained from the crossover exponents, in contrast to multifractals, the asymptotic form of this angular-structure factor is described by the Legendre transform of the (analytically continued) infinite set of crossover exponents only in the special case of two dimensions.

Physical review. B, Condensed matterApr 1, 19899 citations

We study the crossover between two- and three-dimensional behaviors of the Villain form of the XY spin model on a three-dimensional lattice with anisotropic couplings

{\mathit{J}}_{1}

{\mathit{J}}_{2}

=J,

{\mathit{J}}_{3}

=\ensuremath{\alpha}J (0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1). The \ensuremath{\alpha} dependence of various quantities is examined by means of duality transformations, Migdal renormalization group, and Monte Carlo simulations. For the specific heat, a crossover into the Kosterlitz-Thouless behavior takes place around \ensuremath{\alpha}\ensuremath{\simeq}0.2, which corresponds to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{cos}}$\ensuremath{\simeq}0.015 in the cosine form of the XY model. Some implications for models of high-

{\mathit{T}}_{\mathit{c}}

superconductivity are discussed.