### Abstract

*T*= 0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/

*z*) (i.e. beyond mean field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field

*H*. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is strictly positive everywhere inside). On the other hand, the occurrence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied fields, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.

Original language | English |
---|---|

Article number | P03003 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2009 |

Issue number | March 2009 |

DOIs | |

Publication status | Published - Mar 2009 |

Externally published | Yes |

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### Cite this

*T*= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states.

*Journal of Statistical Mechanics: Theory and Experiment*,

*2009*(March 2009), [P03003]. https://doi.org/10.1088/1742-5468/2009/03/P03003

}

*T*= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states',

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2009, no. March 2009, P03003. https://doi.org/10.1088/1742-5468/2009/03/P03003

**The T = 0 random-field Ising model on a Bethe lattice with large coordination number : hysteresis and metastable states.** / Rosinberg, Martin L.; Tarjus, Gilles; Perez-Reche, Francisco J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The T = 0 random-field Ising model on a Bethe lattice with large coordination number

T2 - hysteresis and metastable states

AU - Rosinberg, Martin L.

AU - Tarjus, Gilles

AU - Perez-Reche, Francisco J.

PY - 2009/3

Y1 - 2009/3

N2 - In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T = 0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is strictly positive everywhere inside). On the other hand, the occurrence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied fields, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.

AB - In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T = 0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is strictly positive everywhere inside). On the other hand, the occurrence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied fields, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.

U2 - 10.1088/1742-5468/2009/03/P03003

DO - 10.1088/1742-5468/2009/03/P03003

M3 - Article

VL - 2009

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - March 2009

M1 - P03003

ER -

*T*= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states. Journal of Statistical Mechanics: Theory and Experiment. 2009 Mar;2009(March 2009). P03003. https://doi.org/10.1088/1742-5468/2009/03/P03003