Extension to order $\beta^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Linked cluster expansions provide a useful tool for both analytical and numerical investigations of lattice field theories. The expansion parameter(s) being the interaction strength(s) fields at neighboured lattice sites are coupled, they result into convergent hopping parameter like series for free energies, correlation functions and in particular susceptibilities. We consider scalar fields with O(N) symmetric nearest neighbour interactions on hypercubic lattices with possib...

High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these quantities enter into a sequence of universal amplitude-ratios which determine the critical equation of state. We have obtained a substantial extension through order 24, of the high-temperature expansions of the free energy (in presence of a magneti...

We have computed through order $\beta^{21}$ the high-temperature expansions for the nearest-neighbor spin correlation function $G(N,\beta)$ of the classical N-vector model, with general N, on the simple-cubic and on the body-centered-cubic lattices. For this model, also known in quantum field theory as the lattice O(N) nonlinear sigma model, we have presented in previous papers extended expansions of the susceptibility, of its second field derivative and of the second momen...

We calculate the high-temperature series of the magnetic susceptibility and the second and fourth moments of the correlation function for the XY model on the square lattice to order $\beta^{33}$ by applying the improved algorithm of the finite lattice method. The long series allow us to estimate the inverse critical temperature as $\beta_c=1.1200(1)$, which is consistent with the most precise value given previously by the Monte Carlo simulation. The critical exponent for the ...

We report a quasi-exact power law behavior for Ising critical temperatures on hypercubes. It reads $J/k_BT_c=K_0[(1-1/d)(q-1)]^a$ where $K_0=0.6260356$, $a=0.8633747$, $d$ is the space dimension, $q$ the coordination number ($q=2d$), $J$ the coupling constant, $k_B$ the Boltzman constant and $T_c$ the critical temperature. Absolute errors from available exact estimates ($d=2$ up to $d=7$) are always less than $0.0005$. Extension to other lattices is discussed.

High temperature expansions for the free energy, the susceptibility and the second correlation moment of the classical N-vector model [also denoted as the O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear sigma model] have been extended to order beta^{21} on the simple cubic and the body centered cubic lattices, for arbitrary N. The series for the second field derivative of the susceptibility has been extended to order beta^{17}. An analysis of t...

High temperature expansions for the susceptibility and the second correlation moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For N= 2,3,4.. we present revised estimates of the critical parameters from the newly computed coefficients.

In the Ising model on the simple cubic lattice, we describe the inverse temperature $\beta$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of those quantities are represented by the linear differential equations with constant coefficients which are related to critical exponents. We estimate the critical temperature and exponents via an expansion in the inverse powers of the mass und...

We report computations of the short-distance and the long-distance (scaling) contributions to the square-lattice Ising susceptibility in zero field close to T_c. Both computations rely on the use of nonlinear partial difference equations for the correlation functions. By summing the correlation functions, we give an algorithm of complexity O(N^6) for the determination of the first N series coefficients. Consequently, we have generated and analysed series of length several hun...

A simple systematic rule, inspired by high-temperature series expansion (HTSE) results, is proposed for optimizing the expression for thermodynamic observables of ferromagnets exhibiting critical behavior at $\Tc$. This ``extended scaling'' scheme leads to a protocol for the choice of scaling variables, $\tau=(T-\Tc)/T$ or $(T^2 - \Tc^2)/T^2$ depending on the observable instead of $(T-\Tc)/\Tc$, and more importantly to temperature dependent non-critical prefactors for each ob...