Criticality of Spin Systems with Weak Long-Range Interactions
arXiv:1908.05158 · doi:10.1088/1751-8121/ab6a6c
Abstract
The study of critical properties of systems with long-range interactions has attracted in the last decades a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical spin models and we then move to quantum spin systems.
arXiv comment24 pages, 5 figures, Submitted to the special issue of J. Phys. A on 'Long-range Interactions and Synchronization'
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