Villain model with long-range couplings

Year: 2023

Authors: Giachetti G., Defenu N., Ruffo S., Trombettoni A.

Autors Affiliation: SISSA, Via Bonomea 265, I-34136 Trieste, Italy; INFN Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, Zurich, Switzerland; CNR, Ist Sistemi Complessi, Via Madonna Piano 10, I-50019 Sesto Fiorentino, Italy; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy.

Abstract: The nearest-neighbor Villain, or periodic Gaussian, model is a useful tool to understand the physics of the topological defects of the two-dimensional nearest-neighbor XY model, as the two models share the same symmetries and are in the same universality class. The long-range counterpart of the two-dimensional XY has been recently shown to exhibit a non-trivial critical behavior, with a complex phase diagram including a range of values of the power-law exponent of the couplings decay, sigma, in which there are a magnetized, a disordered and a critical phase [1]. Here we address the issue of whether the critical behavior of the two-dimensional XY model with long-range couplings can be described by the Villain counterpart of the model. After introducing a suitable generalization of the Villain model with long-range couplings, we derive a set of renormalization-group equations for the vortex-vortex potential, which differs from the one of the long-range XY model, signaling that the decoupling of spin-waves and topological defects is no longer justified in this regime. The main results are that for sigma < 2 the two models no longer share the same universality class. Remarkably, within a large region of its the phase diagram, the Villain model is found to behave similarly to the one-dimensional Ising model with 1/r(2) interactions. Journal/Review: JOURNAL OF HIGH ENERGY PHYSICS

Volume: (2)      Pages from: 238-1  to: 238-25

More Information: This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster). The work is part of the MIUR-PRIN2017 project Coarse-grained descrip tion for nonequilibrium systems and transport phenomena (CO-NEST) No. 201798CZL. The authors acknowledge the MISTI Global Seed Funds MIT-FVG collaboration grants NV centers for the test of the Quantum Jarzynski Equality (NVQJE)and Non-Equilibrium Thermodynamics of Dissipative Quantum Systems.
KeyWords: Phase Transitions; Spontaneous Symmetry Breaking; Lattice Integrable Models
DOI: 10.1007/JHEP02(2023)238

Citations: 1
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