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Register a new userSupersymmetric Quantum Spherical Spins with Short-Range Interactions
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Ladislau Vieira Teixeira Tavares
Publication date
2019
fields
Physics
and research's language is
English
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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 $O(N)$ nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large $N$ limit.
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Galam reshuffling introduced in opinion dynamics models is investigated under the nearest neighbor Ising model on a square lattice using Monte Carlo simulations. While the corresponding Galam analytical critical temperature T_C approx 3.09 [J/k_B] is recovered almost exactly, it is proved to be different from both values, not reshuffled (T_C=2/arcsinh(1) approx 2.27 [J/k_B]) and mean-field (T_C=4 [J/k_B]). On this basis, gradual reshuffling is studied as function of 0 leq p leq 1 where p measures the probability of spin reshuffling after each Monte Carlo step. The variation of T_C as function of p is obtained and exhibits a non-linear behavior. The simplest Solomon network realization is noted to reproduce Galam p=1 result. Similarly to the critical temperature, critical exponents are found to differ from both, the classical Ising case and the mean-field values.
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