https://doi.org/10.1140/epjb/s10051-025-00980-9
Topical Review - Statistical and Nonlinear Physics
Ising ferromagnet and nonadditive entropies: equilibrium and nonequilibrium properties
1
Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
2
Santa Fe Institute, 1399 Hyde Park Road, 87501, Santa Fe, NM, USA
3
Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080, Vienna, Austria
Received:
9
April
2025
Accepted:
2
June
2025
Published online:
17
June
2025
Some equilibrium and nonequilibrium properties of the one-dimensional nearest-neighbor Ising ferromagnet that are grounded on nonadditive entropies are reviewed. First, we focus on the known fact that the nonadditive entropy 
for a special value of q, namely 
, yields entropic extensivity, thus satisfying the Legendre structure of classical thermodynamics, at the quantum critical point of the spin-1/2 ferromagnetic Ising chain in the presence of an external transverse field. Then we address a well-known issue in phase transitions, namely that, at the critical point, quantities such as the susceptibility and the Grüneisen ratio diverge within Boltzmann–Gibbs statistical mechanics (
). Moreover, we show that such thermostatistical quantities diverge for 
, vanish for 
, and are finite for 
. Second, we focus on a transport phenomenon, specifically, the heat transport in a one-dimensional Ising model. We do so by analyzing two classical inertial anisotropic XY models that recover the equilibrium and nonequilibrium properties of the Ising model under the extreme anisotropy limit. In other words, we determine, from first principles, the thermal conductivity behavior of the Ising chain with regard to temperature and lattice size, concluding that the model exhibits normal heat conduction, i.e., it satisfies Fourier’s law.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
