Finite-size scaling analysis of three dimensional Z(2) and O(2) spin models with non-vanishing symmetry breaking parameter
Abstract
We present results from a detailed finite-size scaling analysis of the $3−d$, Z(2) and O(2) spin models in an external field H. Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to z̃L2=1/(H L3/(1+1/δ)))2. This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing H. In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3−d$, O(2) and Z(2) universality classes.
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BibTeX
@misc{goswami2026finitesize,
title = {{Finite-size scaling analysis of three dimensional Z(2) and O(2) spin models with non-vanishing symmetry breaking parameter}},
author = {Jishnu Goswami and Frithjof Karsch and Sabarnya Mitra},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10350},
eprint = {2610.10350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10350},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Finite-size scaling analysis of three dimensional Z(2) and O(2) spin models with non-vanishing symmetry breaking parameter
AU - Jishnu Goswami
AU - Frithjof Karsch
AU - Sabarnya Mitra
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10350
UR - https://arxiv.org/abs/2610.10350
AB - We present results from a detailed finite-size scaling analysis of the $3−d$, Z(2) and O(2) spin models in an external field H. Using high statistics Monte Carlo data, we obtain the leading finite-size scaling correction to the infinite volume scaling functions. We show that these corrections are proportional to z̃_L^2=1/(H L^3/(1+1/δ)))^2. This provides the parametric form for finite-size corrections to bulk thermodynamic observables as well as the pseudo-critical temperatures determined at non-vanishing H. In particular, it allows to eliminate systematic errors in the analysis of the chiral phase transition temperature in (2+1)-flavor QCD, that arose from the previously not well-controlled ansatz for infinite volume extrapolations. We also establish the validity range of this leading order correction and point out that there are significant differences between the $3−d$, O(2) and Z(2) universality classes.
ER -