https://doi.org/10.1140/epjb/s10051-026-01199-y
Research - Condensed Matter
Finite-temperature antiferromagnetic correlations and doping effects in the square-lattice Hubbard model
Department of Physics, Amity Institute of Applied Sciences, Amity University Kolkata, Major Arterial Road, Action Area II, 700135, Kolkata, West Bengal, India
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
31
March
2026
Accepted:
1
June
2026
Published online:
29
June
2026
Abstract
We investigate finite-temperature antiferromagnetic correlations in the two-dimensional square-lattice Hubbard model using determinant quantum Monte Carlo simulations. Magnetic properties are analyzed through the antiferromagnetic structure factor 
, real-space spin correlations, correlation-length extraction, and finite-size scaling. At half filling, the antiferromagnetic structure factor increases strongly with inverse temperature for interaction strengths 
–8, reflecting the rapid enhancement of staggered spin correlations upon cooling. Real-space correlations exhibit a clear staggered oscillatory structure with an approximately exponential decay. Semi-logarithmic analysis of the staggered correlations reveals a rapidly increasing effective correlation length 
with decreasing temperature. For sufficiently low temperatures, becomes comparable to the lattice size, indicating the onset of strong finite-size effects rather than true long-range order. Finite-size scaling of 
shows a systematic suppression with increasing system size, consistent with the absence of finite-temperature long-range antiferromagnetic order in accordance with the Mermin–Wagner theorem. Upon doping away from half filling, both the momentum-space structure factor and the real-space staggered correlations are strongly suppressed. The extracted correlation length decreases substantially with doping, demonstrating that mobile carriers weaken the spatial extent of antiferromagnetic correlations. The suppression is observed for both hole and electron doping and is broadly consistent with particle–hole symmetry of the bipartite square lattice. The present results establish a unified finite-temperature picture linking magnetic structure factors, real-space spin correlations, correlation-length growth, and finite-size effects in the square-lattice Hubbard model. Benchmark comparisons with earlier numerical studies further demonstrate quantitative consistency with previously established finite-temperature magnetic trends in the two-dimensional Hubbard model.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-026-01199-y.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
