High-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin $s$ . The fcc lattice is used for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence. It is suggested that the magnetic susceptibility above the Curie temperature is of the form $A{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{4}{3}}$ for the Heisenberg model for all $s$ , instead of ${A}^{\ensuremath{'}}{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{5}{4}}$ for the Ising model. Critical estimates of energy and entropy show that the magnitude of the "tail" of the specific heat anomaly is insensitive to the value of $s$ , and is about 2.5 times larger for the Heisenberg than for the Ising model. The sharpness of the anomaly at the Curie point increases as $s$ increases, and on passing from the Heisenberg to the Ising model. A brief reference is made to experimental results.High-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin $s$. The fcc lattice is used for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence. It is suggested that the magnetic susceptibility above the Curie temperature is of the form $A{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{4}{3}}$ for the Heisenberg model for all $s$, instead of ${A}^{\ensuremath{'}}{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{5}{4}}$ for the Ising model. Critical estimates of energy and entropy show that the magnitude of the "tail" of the specific heat anomaly is insensitive to the value of $s$, and is about 2.5 times larger for the Heisenberg than for the Ising model. The sharpness of the anomaly at the Curie point increases as $s$ increases, and on passing from the Heisenberg to the Ising model. A brief reference is made to experimental results.

Physical ReviewOct 1, 1962213 citations

The Models of Ising and Heisenberg

Walter Greiner, Ludwig Neise, Horst Stöcker B

Springer eBooksJan 1, 19951 citation

The quantum Ising model

Subir Sachdev A

Cambridge University Press eBooksApr 7, 20110 citations

Simulating Heisenberg interactions in the Ising model with strong drive fields

Anthony N. Ciavarella, Stephan Caspar, Hersh Singh +2 more

The time evolution of an Ising model with large driving fields over discrete time intervals is shown to be reproduced by an effective $XXZ$ -Heisenberg model at leading order in the inverse field strength. For specific orientations of the drive field, the dynamics of the $XXX$ -Heisenberg model is reproduced. These approximate equivalences, valid above a critical driving field strength set by dynamical phase transitions in the Ising model, are expected to enable quantum devices that natively evolve qubits according to the Ising model to simulate more complex systems.The time evolution of an Ising model with large driving fields over discrete time intervals is shown to be reproduced by an effective $XXZ$-Heisenberg model at leading order in the inverse field strength. For specific orientations of the drive field, the dynamics of the $XXX$-Heisenberg model is reproduced. These approximate equivalences, valid above a critical driving field strength set by dynamical phase transitions in the Ising model, are expected to enable quantum devices that natively evolve qubits according to the Ising model to simulate more complex systems.

arXiv:2207.09438Physical Review AOct 24, 20236 citations

High-temperature series expansions of the partition functions for the Ising and Heisenberg models are analyzed for various values of the spin

s

. The fcc lattice is used for which successive coefficients are sufficiently regular for estimates of critical behavior to be made with confidence. It is suggested that the magnetic susceptibility above the Curie temperature is of the form $A{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{4}{3}}$ for the Heisenberg model for all

s

, instead of ${A}^{\ensuremath{'}}{(1\ensuremath{-}\frac{{T}_{c}}{T})}^{\ensuremath{-}\frac{5}{4}}$ for the Ising model. Critical estimates of energy and entropy show that the magnitude of the "tail" of the specific heat anomaly is insensitive to the value of

s

, and is about 2.5 times larger for the Heisenberg than for the Ising model. The sharpness of the anomaly at the Curie point increases as

s

increases, and on passing from the Heisenberg to the Ising model. A brief reference is made to experimental results.

The time evolution of an Ising model with large driving fields over discrete time intervals is shown to be reproduced by an effective

XXZ

-Heisenberg model at leading order in the inverse field strength. For specific orientations of the drive field, the dynamics of the

XXX

-Heisenberg model is reproduced. These approximate equivalences, valid above a critical driving field strength set by dynamical phase transitions in the Ising model, are expected to enable quantum devices that natively evolve qubits according to the Ising model to simulate more complex systems.