Critical 1-and 2-point spin correlations for the O(2) model in 3d bounded domains

Year: 2021

Authors: Galvani A., Gori G., Trombettoni A.

Autors Affiliation: SISSA, Via Bonomea 265, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, Via Bonomea 265, I-34136 Trieste, Italy; Heidelberg Univ, Inst Theoret Phys, Philosophenweg 19, D-69120 Heidelberg, Germany; CNR IOM DEMOCRITOS Simulat Ctr, Via Bonomea 265, I-34136 Trieste, Italy; Univ Trieste, Dept Phys, Str Costiera 11, I-34151 Trieste, Italy.

Abstract: We study the critical properties of the 3d O(2) universality class in bounded domains through Monte Carlo simulations of the clock model. We use an improved version of the latter, chosen to minimize finite-size corrections at criticality, with 8 orientations of the spins and in the presence of vacancies. The domain chosen for the simulations is the slab configuration with fixed spins at the boundaries. We obtain the universal critical magnetization profile and two-point correlations, which favorably compare with the predictions of the critical geometry approach based on the Yamabe equation. The main result is that the correlations, once the dimensionful contributions are factored out with the critical magnetization profile, are shown to depend only on the distance between the points computed using a metric found solving the corresponding fractional Yamabe equation. The quantitative comparison with the corresponding results for the Ising model at criticality is shown and discussed. Moreover, from the magnetization profiles the critical exponent eta is extracted and found to be in reasonable agreement with up-to-date results.

Journal/Review: JOURNAL OF HIGH ENERGY PHYSICS

Volume: (10)      Pages from: 106-1  to: 106-17

More Information: The authors thank M. Hasenbusch for useful discussion and correspondence. GG is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2181/1 -390900948 (the Heidelberg STRUCTURES Excellence Cluster). GG also acknowledges QSTAR for hospitality during completion of this work. Stimulating discussions with several participants of Bootstat 2021, held in May in Institut Pascal, Universite Paris-Saclay and online, are also acknowledged.
KeyWords: Boundary Quantum Field Theory; Lattice Quantum Field Theory; Conformal Field Theory
DOI: 10.1007/JHEP10(2021)106

Citations: 1
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2025-09-07
References taken from IsiWeb of Knowledge: (subscribers only)