CRITICAL SPECIFIC HEATS OF THE N-VECTOR SPIN MODELS ON THE SIMPLE CUBIC AND BCC LATTICES

摘要: We have computed through order ${\ensuremath{\beta}}^{21}$ the high-temperature expansions for nearest neighbor spin correlation function $G(N,\ensuremath{\beta})$ of classical N-vector model, with general N, on simple cubic and body centered lattices. For this also known in quantum field theory as lattice $O(N)$ nonlinear $\ensuremath{\sigma}$ we presented previous papers extended susceptibility, its second derivative, moment function. Here study internal specific energy heat $C(N,\ensuremath{\beta}),$ obtaining updated estimates critical parameters therefore a more accurate direct test hyperscaling relation $d\ensuremath{\nu}(N)=2\ensuremath{-}\ensuremath{\alpha}(N)$ range values dimensionality including $N=0$ (the self-avoiding walk model), $N=1$ Ising 1/2 $N=2$ $\mathrm{XY}$ $N=3$ Heisenberg model). By newly series compute universal combination amplitudes usually denoted by ${R}_{\ensuremath{\xi}}^{+}(N),$ fair agreement renormalization group estimates.