Total spin asymptotic normality at the critical point for a classical statistical physics model
It is presented a lattice model with a Hamiltonian given by the formula \[ H_\Lambda^{\beta,h} (x/ \overline x) ={\beta\over 2} \sum_{t,s\in \Lambda, \|t-s\|=1} |x_t||x_s|+ \beta\sum_{t\in \Lambda, s\in \partial\Lambda} |x_t| |\overline x_s| +h\sum_{t\in \Lambda} |x_t|, \] \(x_t,x_s\in X=\{-1,0,1\},\) \(t,s\in Z^\nu\), \(h\in R^1\), \(\beta>0\), \(x\in X^\Lambda\), \(\overline x\in X^{\partial \Lambda}\). It is shown that in this model there is a phase transition on the line \(h+\beta \nu-\ln 2=0\) and that the total spin at the critical point has non-standard behaviour, i.e. the central limit theorem is valid.
scientific article; zbMATH DE number 1190936