Numerical study of phase diagram and reentrance in random spin systems without gauge symmetry

We introduce a class of random spin systems without frustration, which satisfies the conditions for gauge symmetry. The method of gauge transformation provides several properties on the phase diagram of gauge symmetric models; this method is almost rigorous, while the derivation for the absence of re-entrance contains unproved assumption. In the present random models, the absence of re-entrance can be shown exactly. Furthermore, the phase diagram and the critical properties are exactly related with those in the original pure system. The present random systems correspond to the Mattis model with asymmetric bond distribution in the Ising case, and a kind of the gauge glass model in the XY case. In the case of the clock model in two dimensions, we find a new thermodynamic phase which has long-range spin-glass correlation with critical (power-decaying) ferromagnetic correlation.We introduce a class of random spin systems without frustration, which satisfies the conditions for gauge symmetry. The method of gauge transformation provides several properties on the phase diagram of gauge symmetric models; this method is almost rigorous, while the derivation for the absence of re-entrance contains unproved assumption. In the present random models, the absence of re-entrance can be shown exactly. Furthermore, the phase diagram and the critical properties are exactly related with those in the original pure system. The present random systems correspond to the Mattis model with asymmetric bond distribution in the Ising case, and a kind of the gauge glass model in the XY case. In the case of the clock model in two dimensions, we find a new thermodynamic phase which has long-range spin-glass correlation with critical (power-decaying) ferromagnetic correlation.

Journal of Physics A Mathematical and GeneralSep 21, 19963 citations

The Method of Gauge Transformation in Random Spin Systems

之康尾関, Yukiyasu Ozeki

Jan 1, 19960 citations

Strongly Asymmetric Tricriticality of Quenched Random-Field Systems

Alkan Kabakçıoğlu, A. Nihat Berker

In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random magnetic fields on the tricritical phase diagram of the spin-1 Ising model in $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ . We find that random fields convert first-order phase transitions into second-order phase transitions more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent ${\ensuremath{\beta}}_{u}$. The random-field phase diagram is strikingly asymmetric. To accommodate this asymmetry, the second-order boundary exhibits reentrance.In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random magnetic fields on the tricritical phase diagram of the spin-1 Ising model in $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$. We find that random fields convert first-order phase transitions into second-order phase transitions more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent ${\ensuremath{\beta}}_{u}$. The random-field phase diagram is strikingly asymmetric. To accommodate this asymmetry, the second-order boundary exhibits reentrance.

arXiv:cond-mat/9811235Physical Review LettersMar 22, 19997 citations

Numerical Study of Quantum Spin Systems

Makoto Kaburagi, Takashi Tonegawa, T. Nishino

Springer proceedings in physicsJan 1, 19925 citations

Inverse freezing in the Hopfield fermionic Ising spin glass

S. G. Magalhães, C.V. Morais, Fábio M. Zimmer

In this work we studied the Hopfield fermionic spin-glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic-disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime, and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path-integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The grand canonical potential is obtained within the static approximation and one-step replica symmetry-breaking scheme. As a result, phase diagrams temperature versus the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed.In this work we studied the Hopfield fermionic spin-glass model which allows interpolating from trivial randomness to a highly frustrated regime. Therefore, it is possible to investigate whether or not frustration is an essential ingredient which would allow this magnetic-disordered model to present naturally inverse freezing by comparing the two limits, trivial randomness and highly frustrated regime, and how different levels of frustration could affect such unconventional phase transition. The problem is expressed in the path-integral formalism where the spin operators are represented by bilinear combinations of Grassmann variables. The grand canonical potential is obtained within the static approximation and one-step replica symmetry-breaking scheme. As a result, phase diagrams temperature versus the chemical potential are obtained for several levels of frustration. Particularly, when the level of frustration is diminished, the reentrance related to the inverse freezing is gradually suppressed.

arXiv:0912.4469Physical Review BJan 15, 201011 citations

d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3

. We find that random fields convert first-order phase transitions into second-order phase transitions more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent ${\ensuremath{\beta}}_{u}$. The random-field phase diagram is strikingly asymmetric. To accommodate this asymmetry, the second-order boundary exhibits reentrance.