SMJ's analysis of Ising model correlation functions

Gesualdo Delfino A, Giuseppe Mussardo, P. Simonetti

A nonperturbative method based on the form factor bootstrap approach is proposed for the analysis of correlation functions of two-dimensional massless integrable theories and applied to the massless flow between the tricritical Ising and the critical Ising models.

C. Ruge, P. Zhu, F. Wagner

V. N. Plechko

The anticommuting analysis with Grassmann variables is applied to the two-dimensional Ising model in statistical mechanics. The discussion includes the transformation of the partition function into a Gaussian fermionic integral, the momentum-space representation and the spin-fermion correspondence at the level of the correlation functions.

M. Helm

Pik-Yin Lai, K. K. Mon

We report extensive Monte Carlo simulations and finite-size scaling analysis of the correlation length (${\ensuremath{\xi}}_{\mathrm{L}}$) for the spin-spin correlation function and the renormalized coupling (${\mathrm{g}}_{\mathrm{L}}$) of the simple-cubic Ising model with a wide range of lattice sizes (L\ensuremath{\le}96). New methods of analysis which avoid assumptions related to the correlation length were introduced. The exponents \ensuremath{\nu} and 2-\ensuremath{\alpha} were estimated from separate analysis of ${\ensuremath{\xi}}_{\mathrm{L}}$ and ${\mathrm{g}}_{\mathrm{L}}$, respectively. A value of ${\mathrm{\ensuremath{\omega}}}^{\mathrm{*}}$\ensuremath{\approxeq}0.001\ifmmode\pm\else\textpm\fi{}0.07 for the Fisher exponent is obtained. This is consistent with a very small or no violations of hyperscalings.

G. V. Ryazanov