Abstract
Universality is a pillar of modern critical phenomena. The standard scenario is that the two-point correlation algebraically decreases with the distance as , with the spatial dimension and the anomalous dimension. Very recently, a logarithmic universality was proposed to describe the extraordinary surface transition of the system. In this logarithmic universality, decays in a power of logarithmic distance as , dramatically different from the standard scenario. We explore the three-dimensional model by Monte Carlo simulations, and provide strong evidence for the emergence of logarithmic universality. Moreover, we propose that the finite-size scaling of has a two-distance behavior: simultaneously containing a large-distance plateau whose height decays logarithmically with as as well as the -dependent term , with . The critical exponent , characterizing the height of the plateau, obeys the scaling relation with the RG parameter 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.
- Received 11 April 2021
- Revised 23 May 2021
- Accepted 11 August 2021
DOI:https://doi.org/10.1103/PhysRevLett.127.120603
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