Thermodynamics of the HMF model with a magnetic field |
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Authors: | P H Chavanis |
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Institution: | 1.Laboratoire de Physique Théorique (IRSAMC), CNRS and UPS, Université de Toulouse,Toulouse,France |
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Abstract: | We study the thermodynamics of the Hamiltonian mean field
(HMF) model with an external potential playing the role of a
“magnetic field”. If we consider only fully stable states,
the caloric curve does not present any phase
transition. However, if we take into account metastable states (for
a restricted class of perturbations), we find a very rich
phenomenology. In particular, the caloric curve
displays a region of negative specific heat in the microcanonical
ensemble in which the temperature decreases as the energy
increases. This leads to ensembles inequivalence and to zeroth
order phase transitions similar to the “gravothermal catastrophe”
and to the “isothermal collapse” of self-gravitating systems. In
the present case, they correspond to the reorganization of the
system from an “anti-aligned” phase (magnetization pointing in
the direction opposite to the magnetic field) to an “aligned”
phase (magnetization pointing in the same direction as the magnetic
field). We also find that the magnetic susceptibility can be
negative in the microcanonical ensemble so that the magnetization
decreases as the magnetic field increases. The magnetic curves can
take various shapes depending on the values of energy or temperature. We
describe first order phase
transitions and hysteretic cycles involving positive or negative
susceptibilities. We also show that this model exhibits gaps in the
magnetization at fixed energy, resulting in ergodicity breaking. |
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Keywords: | |
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