We calculate the thermodynamics of the one-dimensional spin-1/2 Ising model in the presence of a constant skew magnetic field. We obtain the high-temperature expansion of its Helmholtz free energy (HFE), for the ferromagnetic and antiferromagnetic cases, up to order beta7. This expansion permits us to obtain the behaviour of the model for $ |J| \beta \stackrel {<}{_\sim}} 1 $, when it cannot be described by its classical version. Among the calculated thermodynamical functions of the model, we have the diagonal elements of the magnetic susceptibility tensor for the transverse and logitudinal Ising models, obtained by taking the limits h z -> 0 and h y -> 0, respectively, of the beta-expansion of the HFE. The y-component of the magnetization and the chiyy component of the magnetic susceptibility tensor are almost the same for the antiferro- and ferromagnetic models, at least for $ |J| \beta \stackrel {<}{_\sim}} 1 $; and, c yy is practically independent of the direction of the external magnetic. We also show that, in this region of temperature, the thermodynamics of the Ising model with skew magnetic field and that of an XXZ model with longitudinal magnetic field are not similar.We calculate the thermodynamics of the one-dimensional spin-1/2 Ising model in the presence of a constant skew magnetic field. We obtain the high-temperature expansion of its Helmholtz free energy (HFE), for the ferromagnetic and antiferromagnetic cases, up to order beta7. This expansion permits us to obtain the behaviour of the model for $ |J| \beta \stackrel {<}{_\sim}} 1 $, when it cannot be described by its classical version. Among the calculated thermodynamical functions of the model, we have the diagonal elements of the magnetic susceptibility tensor for the transverse and logitudinal Ising models, obtained by taking the limits h z -> 0 and h y -> 0, respectively, of the beta-expansion of the HFE. The y-component of the magnetization and the chiyy component of the magnetic susceptibility tensor are almost the same for the antiferro- and ferromagnetic models, at least for $ |J| \beta \stackrel {<}{_\sim}} 1 $; and, c yy is practically independent of the direction of the external magnetic. We also show that, in this region of temperature, the thermodynamics of the Ising model with skew magnetic field and that of an XXZ model with longitudinal magnetic field are not similar.

Brazilian Journal of PhysicsMar 1, 20082 citations

Quantum Otto and Carnot Cycles via Skew Ising Model

Neda Valizadeh, Nayyere Einali Saghavaz, Zahra Ebadi +1 more

Abstract We investigate the thermodynamic performance of quantum heat engines and refrigerators based on a two-spin system subject to a skew magnetic field. The working substance is described by an interacting spin model that incorporates both spin--spin coupling and anisotropy induced by a tilted magnetic field. We analyze and compare quantum Carnot and Otto cycles, showing that the Carnot cycle exhibits a universal, entropy-driven behavior with smooth phase boundaries, while the Otto cycle displays a much richer structure governed by the interplay between the energy spectrum and nonequilibrium population differences. In particular, we identify a crossover in both efficiency and coefficient of performance as a function of the interaction strength, which arises from the competition between the interaction energy scale and the magnetic field. We further demonstrate that the skew angle induces state hybridization, modifying both the energy levels and occupation probabilities. Our results highlight that interactions and anisotropy, when properly tuned, can enhance thermodynamic performance, and emphasize the importance of multi-level effects in the design of quantum thermal machines.Abstract We investigate the thermodynamic performance of quantum heat engines and refrigerators based on a two-spin system subject to a skew magnetic field. The working substance is described by an interacting spin model that incorporates both spin--spin coupling and anisotropy induced by a tilted magnetic field. We analyze and compare quantum Carnot and Otto cycles, showing that the Carnot cycle exhibits a universal, entropy-driven behavior with smooth phase boundaries, while the Otto cycle displays a much richer structure governed by the interplay between the energy spectrum and nonequilibrium population differences. In particular, we identify a crossover in both efficiency and coefficient of performance as a function of the interaction strength, which arises from the competition between the interaction energy scale and the magnetic field. We further demonstrate that the skew angle induces state hybridization, modifying both the energy levels and occupation probabilities. Our results highlight that interactions and anisotropy, when properly tuned, can enhance thermodynamic performance, and emphasize the importance of multi-level effects in the design of quantum thermal machines.

arXiv:2606.09911Aug 31, 20260 citations

Spin- Ising model in a staggered magnetic field

A. Benyoussef, T. Biaz, M. Touzani

Physics Letters ASep 1, 19892 citations

Decay of the metastable phase in d = 1 and d = 2 Ising models

S. B. Rutkevich

We calculate perturbatively the tunneling decay rate $\ensuremath{\Gamma}$ of the metastable phase in the quantum $d=1$ Ising model in a skew magnetic field near the coexistence line $0<{h}_{x}<1, {h}_{z}\ensuremath{\rightarrow}\ensuremath{-}0$ at $T=0.$ It is shown that $\ensuremath{\Gamma}$ oscillates in the magnetic field ${h}_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic $d=2$ Ising model at $T<{T}_{c},$ we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We also find evidence for the discrete-lattice corrections in this metastable phase free energy.We calculate perturbatively the tunneling decay rate $\ensuremath{\Gamma}$ of the metastable phase in the quantum $d=1$ Ising model in a skew magnetic field near the coexistence line $0<{h}_{x}<1, {h}_{z}\ensuremath{\rightarrow}\ensuremath{-}0$ at $T=0.$ It is shown that $\ensuremath{\Gamma}$ oscillates in the magnetic field ${h}_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic $d=2$ Ising model at $T<{T}_{c},$ we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We also find evidence for the discrete-lattice corrections in this metastable phase free energy.

arXiv:cond-mat/9904059Physical review. B, Condensed matterDec 1, 199949 citations

We calculate perturbatively the tunneling decay rate $\ensuremath{\Gamma}$ of the metastable phase in the quantum

d=1

Ising model in a skew magnetic field near the coexistence line $0<{h}_{x}<1, {h}_{z}\ensuremath{\rightarrow}\ensuremath{-}0$ at

T=0.

It is shown that $\ensuremath{\Gamma}$ oscillates in the magnetic field

{h}_{z}

due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic

d=2

Ising model at

T<{T}_{c},

we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We also find evidence for the discrete-lattice corrections in this metastable phase free energy.