Finite-size scaling of O(n) systems at the upper critical dimensionality.

ABSTRACT: Logarithmic finite-size scaling of the O(n) universality class at the upper critical dimensionality (d _c = 4) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the n-vector model (n = 1, 2, 3) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free-energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation g(r, L), with L the linear size, exhibits a two-length behavior: foll

SUBMITTER: Lv JP 

PROVIDER: S-EPMC8288422 | biostudies-literature | 2021 Mar

REPOSITORIES: biostudies-literature