Critical behavior of an Ising model of classical spins in a transverse field

Abstract

The critical behavior of an Ising model of classical spins in a transverse field $H$ is derived for dimension $d=4-\epsilon$ using an $\epsilon$ expansion based on the Wilson renormalization group. To first order in $\epsilon$ the model exhibits a line of critical points $T_c\mathrm{}\left(H\right)\mathrm{}$ with the same fixed point and critical exponents as in previous studies of the Wilson effective Hamiltonian.