Abstract
This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z = 2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.
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