Extraordinary-Log Surface Phase Transition in the Three-Dimensional XY Model

Minghui Hu, Youjin Deng, and Jian-Ping Lv
Phys. Rev. Lett. 127, 120603 – Published 16 September 2021
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Abstract

Universality is a pillar of modern critical phenomena. The standard scenario is that the two-point correlation algebraically decreases with the distance r as g(r)r2dη, with d the spatial dimension and η the anomalous dimension. Very recently, a logarithmic universality was proposed to describe the extraordinary surface transition of the O(N) system. In this logarithmic universality, g(r) decays in a power of logarithmic distance as g(r)(lnr)η^, dramatically different from the standard scenario. We explore the three-dimensional XY model by Monte Carlo simulations, and provide strong evidence for the emergence of logarithmic universality. Moreover, we propose that the finite-size scaling of g(r,L) has a two-distance behavior: simultaneously containing a large-distance plateau whose height decays logarithmically with L as g(L)(lnL)η^ as well as the r-dependent term g(r)(lnr)η^, with η^η^1. The critical exponent η^, characterizing the height of the plateau, obeys the scaling relation η^=(N1)/(2πα) with the RG parameter α of helicity modulus. Our picture can also explain the recent numerical results of a Heisenberg system. The advances on logarithmic universality significantly expand our understanding of critical universality.

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  • Received 11 April 2021
  • Revised 23 May 2021
  • Accepted 11 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.120603

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Minghui Hu1, Youjin Deng2,3,*, and Jian-Ping Lv1,†

  • 1Department of Physics and Anhui Key Laboratory of Optoelectric Materials Science and Technology, Key Laboratory of Functional Molecular Solids, Ministry of Education, Anhui Normal University, Wuhu, Anhui 241000, China
  • 2Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 3MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China

  • *yjdeng@ustc.edu.cn
  • jplv2014@ahnu.edu.cn

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Issue

Vol. 127, Iss. 12 — 17 September 2021

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