An Exact Renormalisation in a Vertex Model

Carlos S. O. Yokoi, Silvio R. A. Salinas

Bernard Nienhuis, Eberhard K. Riedel, Michael Schick C

The results of a variational renormalisation-group calculation for the magnetic exponent y H of the two-dimensional q-state Potts model suggest a simple relationship between y H and the exactly known critical exponent y T 8v of the eight-vertex model. The relation allows one to predict the critical and tricritical magnetic exponent delta of the q-state Potts model as a function of q.

Yu. A. Izyumov, Jon Henderson

We include an additional diagram in the bare electron-electron vertex within the generalised random phase approximation (GRPA) for the t-J model. The equation for the effective electron-electron vertex becomes more complicated but is solved exactly for the simple cubic lattice. The dynamical magnetic susceptibility obtained is the same as in GRPA but with all quantities renormalised. Instability of the paramagnetic phase with respect to the formation of ferromagnetic or antiferromagnetic ordering is studied. Formulae for Curie and Neel temperatures are obtained. The additional diagram leads to an extension of the antiferromagnetic region and a reduction in the ferromagnetic region.

H. J. F. Knops

Arthur Layzer

M. Aydin, M. Cemal Yalabık

The dynamical critical exponent z is obtained through a Monte Carlo renormalisation group calculation for the eight-vertex model with non-conserved dynamics. The value of z at several points along the critical line is evaluated. No appreciable variation in z relative to the Ising value is observed within the accuracy of the work.