### Abstract

We compute the moments of this probability distribution on the space of measures and show in particular that it is not Gaussian.

Language | English |
---|---|

Pages | 585-606 |

Number of pages | 22 |

Journal | Markov Processes and Related Fields |

Volume | 10 |

Issue number | 4 |

Publication status | Published - 2004 |

### Fingerprint

### Keywords

- spin glasses
- frustrated spin systems
- probability measures on infinite-dimensional spaces
- limit theorems
- occupation measures

### Cite this

*Markov Processes and Related Fields*,

*10*(4), 585-606.

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*Markov Processes and Related Fields*, vol. 10, no. 4, pp. 585-606.

**Fluctuations of the local magnetic field in frustrated mean-field Ising models.** / Dukes, W.M.B.; Dorlas, Tony.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fluctuations of the local magnetic field in frustrated mean-field Ising models

AU - Dukes, W.M.B.

AU - Dorlas, Tony

PY - 2004

Y1 - 2004

N2 - We consider fluctuations of the local magnetic field in frustrated mean-field Ising models. Frustration can come about due to randomness of the interaction as in the Sherrington - Kirkpatrick model, or through fixed interaction parameters but with varying signs. We consider central limit theorems for the fluctuation of the local magnetic field values w.r.t. the a priori spin distribution for both types of models. We show that, in the case of the Sherrington - Kirkpatrick model there is a central limit theorem for the local magnetic field, a.s. with respect to the randomness. On the other hand, we show that, in the case of non-random frustrated models, there is no central limit theorem for the distribution of the values of the local field, but that the probability distribution of this distribution does converge.We compute the moments of this probability distribution on the space of measures and show in particular that it is not Gaussian.

AB - We consider fluctuations of the local magnetic field in frustrated mean-field Ising models. Frustration can come about due to randomness of the interaction as in the Sherrington - Kirkpatrick model, or through fixed interaction parameters but with varying signs. We consider central limit theorems for the fluctuation of the local magnetic field values w.r.t. the a priori spin distribution for both types of models. We show that, in the case of the Sherrington - Kirkpatrick model there is a central limit theorem for the local magnetic field, a.s. with respect to the randomness. On the other hand, we show that, in the case of non-random frustrated models, there is no central limit theorem for the distribution of the values of the local field, but that the probability distribution of this distribution does converge.We compute the moments of this probability distribution on the space of measures and show in particular that it is not Gaussian.

KW - spin glasses

KW - frustrated spin systems

KW - probability measures on infinite-dimensional spaces

KW - limit theorems

KW - occupation measures

UR - http://mech.math.msu.su/~malyshev/mprf.htm

M3 - Article

VL - 10

SP - 585

EP - 606

JO - Markov Processes and Related Fields

T2 - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

SN - 1024-2953

IS - 4

ER -