Spontaneous symmetry breaking phenomena in the transverse field mixed $p$ -spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study $\mathbb Z_2$ -symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature are bounded by those on the Nishimori line in the corresponding classical model. These bounds imply that neither ferromagnetic long-range order nor spontaneous magnetization exists in spin glass phase. It is proven also that the ferromagnetic susceptibility has an upper bound in paramagnetic and spin glass phases.Spontaneous symmetry breaking phenomena in the transverse field mixed $p$-spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study $\mathbb Z_2$-symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature are bounded by those on the Nishimori line in the corresponding classical model. These bounds imply that neither ferromagnetic long-range order nor spontaneous magnetization exists in spin glass phase. It is proven also that the ferromagnetic susceptibility has an upper bound in paramagnetic and spin glass phases.

arXiv:2305.19630Journal of the Physical Society of JapanMay 31, 20234 citations

Some Aspects of Infinite-Range Models of Spin Glasses: Theory and Numerical Simulations

Alain H. Billoire

Springer eBooksDec 8, 20071 citation

Ising Spin-Glass Transition in a Magnetic Field Outside the Limit of Validity of Mean-Field Theory

Luca Leuzzi, Giorgio Parisi A, Federico Ricci‐Tersenghi +1 more

The spin-glass transition in a magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Evidence for a spin-glass transition in a magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension in a zero magnetic field.The spin-glass transition in a magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to changing the dimension in spin-glass short-range models. Evidence for a spin-glass transition in a magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension in a zero magnetic field.

arXiv:0811.3435Physical Review LettersDec 22, 200979 citations

Correspondence between long-range and short-range spin glasses

R. A. Baños, L. A. Fernández, Víctor Martín-Mayor +1 more

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power $\ensuremath{\sigma}$ of the distance. We show that there is a value of $\ensuremath{\sigma}$ of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of $\ensuremath{\sigma}$ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power $\ensuremath{\sigma}$ of the distance. We show that there is a value of $\ensuremath{\sigma}$ of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of $\ensuremath{\sigma}$ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

arXiv:1207.7014Physical Review BOct 17, 201250 citations

On a theory of spin glasses with finite range of interactions

N. I. Lebedev

Solid State CommunicationsSep 1, 19891 citation

Spontaneous symmetry breaking phenomena in the transverse field mixed

p

-spin glass model in finite dimensions are studied with Nishimori's gauge theory. Useful identities in the gauge theory enable us to study

\mathbb Z_2

-symmetry breaking. It is proven that ferromagnetic long-range order and spontaneous magnetization at an arbitrary temperature are bounded by those on the Nishimori line in the corresponding classical model. These bounds imply that neither ferromagnetic long-range order nor spontaneous magnetization exists in spin glass phase. It is proven also that the ferromagnetic susceptibility has an upper bound in paramagnetic and spin glass phases.