Wilson’s renormalization-group approach to ad-dimensional quantum sine-Gordon model

Abstract

Wilson's renormalization-group method is used for investigating the critical properties and the role of quantum fluctuations for a d-dimensional quantum sine-Gordon model. In the classical regime a phase transition is found in d=2-\ensuremath{\epsilon} (\ensuremath{\epsilon}\ensuremath{\ge}0) dimensions and the static critical exponents are evaluated to leading order in \ensuremath{\epsilon}g0. Within the same formalism, the dynamic critical exponent z is also obtained as a characteristic of the intrinsic dynamics of the model. The quantum regime is briefly discussed, and no phase transition is found for dg1. We argue that a quantum-classical crossover occurs for 1ld\ensuremath{\le}2 in the low-temperature limit as a consequence of a dimensional crossover d\ensuremath{\rightarrow}d+1 which shifts the upper critical dimensionality from ${d}_{\mathrm{cu}}$=2 to ${d}_{\mathrm{cu}}$=1.