SKM 2023 – wissenschaftliches Programm
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MA: Fachverband Magnetismus
MA 23: Poster Magnetism I
MA 23.47: Poster
Dienstag, 28. März 2023, 17:00–19:00, P1
Finite-size scaling for 5D Ising model with free boundary conditions — •Yulian Honchar1,2,3, Bertrand Berche1,4, Yurij Holovatch1,3, and Ralph Kenna1,2 — 1L4 Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe — 2Centre for Fluid and Complex Systems, Coventry University, United Kingdom — 3Institute for Condensed Matter Physics, National Acad. Sci. of Ukraine, Lviv, Ukraine — 4Laboratoire de Physique et Chimie Théoriques, Université de Lorraine - CNRS, Nancy, Vandœuvre les Nancy, France
It is widely known that in systems with dimensionality higher than the upper critical, the scaling exponents assume their mean field values. However, in this case, the hyperscaling relation, which contains the dimensionality of space, is violated. In addition, mean-field exponents do not agree with the finite-size scaling. One of the theories that aimed to theoretically describe the behaviour of a finite-sized system is the Gaussian fixed point (so-called G-scaling) at which the interactions in the Landau-Ginsburg action are put to zero. Monte Carlo simulations of hypercubic lattices in the Ising model, where duc = 4, show that for periodic boundary conditions the exponents of the GFP do not correspond to the FSS. Another theory emerges with the introduction of a new exponent q into hyperscaling, which is equal to 1 for the dimensions d ≤ duc, and q = d / duc for higher dimensions. Q-scaling is confirmed for lattices with PBC. In this work, we investigated FSS on d=5 lattices with free boundary conditions and showed that, unlike in systems with PBC, it is closer to G-scaling.