Spherical Model of a Ferromagnet

Lewis, Howard B.; Wannier, Gregory H.

doi:10.1103/physrev.88.682.2

Cited by 117 publications

(74 citation statements)

References 1 publication

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“…Rather, the dynamical evolution follows path IV leading to low temperature states E which are quite distinct from D. In other words, the system with N = ∞ supports two different low temperature phases, whose realization depends on the order of the limits t → ∞ and N → ∞. The distinction between these two phases is reminiscent of the difference between the zero field low temperature states in the spherical model [12] and in the mean spherical model [13]. In particular, states E are very similar to the low temperature states in the ideal Bose gas, as it will be clarified in the next section.…”

Section: Introductionmentioning

confidence: 97%

Condensation vs phase ordering in the dynamics of first-order transitions

Castellano¹,

Corberi²,

Zannetti³

1997

Phys. Rev. E

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The origin of the non commutativity of the limits t → ∞ and N → ∞ in the dynamics of first order transitions is investigated. In the large-N model, i.e. N → ∞ taken first, the low temperature phase is characterized by condensation of the large wave length fluctuations rather than by genuine phase-ordering as when t → ∞ is taken first. A detailed study of the scaling properties of the structure factor in the large-N model is carried out for quenches above, at and below Tc. Preasymptotic scaling is found and crossover phenomena are related to the existence of components in the order parameter with different scaling properties. Implications for phase-ordering in realistic systems are discussed.

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Section: Introductionmentioning

confidence: 97%

Condensation vs phase ordering in the dynamics of first-order transitions

Castellano¹,

Corberi²,

Zannetti³

1997

Phys. Rev. E

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“…Since the seminal work by Berlin and Kac, 1 it has been widely accepted that classical spherical models [2][3][4] have played an important role in statistical mechanics due to the opportunity they offer to rigorously study properties otherwise uncommonly probed through exact calculations, such as the critical behavior of observables close to thermal phase transitions and finite-size scaling hypotheses, just to name a few. The result by Stanley 5 that the spherical condition maps onto the limit of infinity spin dimensionality of the Heisenberg classical model has provided a way of contact between the spherical model and realistic spin systems.…”

Section: Introductionmentioning

confidence: 99%

Quantum spherical spin model on hypercubic lattices

2006

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We present an alternative treatment to the quantum spherical spin model on ͑d Ն 2͒-dimensional hypercubic lattices, focusing on the effects of quantum ͑g͒ and thermal ͑T͒ fluctuations, under a uniform magnetic field h, on the correlation function, correlation length, entropy, specific heat, and energy gap in the excitation spectrum. Explicit expressions for such quantities are provided close to the d Ն 2 quantum ͑g = g c , T =0͒ and d Ն 3 thermal ͓T = T c ͑g͔͒ phase transitions in h = 0, including the low-T quantum regimes near the quantum critical point. In particular, the calculation of the correlation function and correlation length generalizes the results on the g = 0 classical spherical model. At T = 0, the zero-field system is gapless at and below g c ; however, a gap opens in the quantum-disordered ground state, g Ͼ g c . Conversely, the null gap for T Յ T c ͑g 0͒ becomes finite as T → T c ͑g 0͒ + ; thus, quantum fluctuations suppress the critical prefactors of observables near T c ͑g 0͒, though they are irrelevant to the universality class shared with the gapless classical spherical model. The results on the entropy and specific heat in g 0 circumvent the drawback in classical spherical models concerning the third law of thermodynamics, as T → 0.

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“…Practically it is easier to implement the constraints (4), (5) only in the mean through Lagrange multipliers λ and µ. In the thermodynamic limit N → ∞ it is known that this leads to the same result [18]. The mean spherical Hamiltonian can then be written as…”

Section: The Model: Grand Canonical Partition Function For a System Wmentioning

confidence: 99%

Thermodynamics of a finite system of classical particles with short- and long-range interactions and nuclear fragmentation

Richert

Wagner²,

Henkel³

et al. 1998

Nuclear Physics A

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We describe a finite inhomogeneous three dimensional system of classical particles which interact through short and (or) long range interactions by means of a simple analytic spin model. The thermodynamic properties of the system are worked out in the framework of the grand canonical ensemble. It is shown that the system experiences a phase transition at fixed average density in the thermodynamic limit. The phase diagram and the caloric curve are constructed and compared with numerical simulations. The implications of our results concerning the caloric curve are discussed in connection with the interpretation of corresponding experimental data. : 25.70.Pq, 64.60.Cn, 64.60.Fr PACS

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Spherical Model of a Ferromagnet

Cited by 117 publications

References 1 publication

Condensation vs phase ordering in the dynamics of first-order transitions

Condensation vs phase ordering in the dynamics of first-order transitions

Quantum spherical spin model on hypercubic lattices

Thermodynamics of a finite system of classical particles with short- and long-range interactions and nuclear fragmentation

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