The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent $\ensuremath{\nu}$ in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent $\ensuremath{\nu}$ are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.
We analyze the infrared behavior of effective
N-point interactions between order parameter fluctuations for nematic and other quantum critical electron systems with a scalar order parameter in two dimensions. The interactions exhibit a singular momentum and energy dependence and thus can not be represented by local vertices. They diverge for all $N\ensuremath{\ge}4$ in a collinear low-energy limit, where energy variables scale to zero faster than momenta, and momenta become increasingly collinear. The degree of divergence is not reduced by any cancellations and renders all
N-point interactions marginal. A truncation of the order parameter action at quartic or any other finite order is therefore not justified. The same conclusion can be drawn for the effective action describing fermions coupled to a U
(1) gauge field in two dimensions.
Abstract Non-relativistic conformal field theory is significant to understand various aspects of an ultra-cold system. In this paper, we study a non-relativistic system of two-component fermions interacting with a complex boson with Yukawa-like interactions near d = 4-spatial dimensions in the presence of a quenched disorder. The homogeneous theory flows to an interacting fixed point describing a unitary fermion system. In the presence of the disorder, we find that the system has an interesting phase structure in the space of the coupling constants and exhibits an interacting disorder fixed point in ϵ-expansion. The correlation function obeys Lifshitz scaling behaviour at the disorder fixed point with the anisotropic exponent being z = 2 + γE. We also study the disorder system at finite temperature and compute the leading contribution to the 1PI effective action.