Systems with separable many-particle interactions. II

Ouden, L.W.J. den; Capel, H.W.; Perk, Jacques H. H.; Tindemans, P.A.J.

doi:10.1016/0378-4371(76)90019-4

Cited by 35 publications

(10 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us stress that this non-local mapping does not keep track of state properties as well as degeneracies. However, the QTFIM and its dual are isospectral and we can therefore directly conclude that also H QTFIM dual displays a first-order phase transition in the thermodynamic limit, but in this case between a symmetry unbroken phase with zero magnetization per spin and zero photons per spin at small g and an ordered phase with finite M z and n for large g. These findings are indeed in accordance with general considerations of Rabi Hamiltonians competing with short-range interactions [38,39].…”

Section: Phase Diagramsupporting

confidence: 87%

The Ising model in a light-induced quantized transverse field

Rohn,

Hörmann,

Genes

et al. 2020

Preprint

View full text Add to dashboard Cite

We investigate the influence of light-matter interactions on correlated quantum matter by studying the paradigmatic Ising model subject to a quantum Rabi coupling. This type of coupling to a confined, spatially delocalized bosonic light mode, such as provided by an optical resonator, resembles a quantized transverse magnetic field of tunable strength. As a consequence, the symmetry-broken magnetic state breaks down for strong enough light-mater interactions to a paramagnetic state. The non-local character of the bosonic mode can change the quantum phase transition in a drastic manner, which we analyze quantitatively for the simplest case of a chain geometry (Dicke-Ising chain). The results show a direct transition between a magnetically ordered phase with zero photon density and a magnetically polarized phase with lasing behaviour of the light. Our predictions are equally valid for the dual quantized Ising chain in a conventional transverse magnetic field.

show abstract

Section: Phase Diagramsupporting

confidence: 87%

The Ising model in a light-induced quantized transverse field

Rohn,

Hörmann,

Genes

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Let us make a few remarks on alternative forms for the above equations. First, summing over z the first equation in (20) we obtain thanks to (15)…”

Section: Chain Curie-weiss Modelmentioning

confidence: 99%

Chains of mean-field models

Hassani¹,

Macris²,

Urbanke³

2012

J. Stat. Mech.

View full text Add to dashboard Cite

We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of the chain and by an infinite range interaction in the direction transverse to the chain. Our motivations for studying this model come from recent findings in the theory of error correcting codes based on spatially coupled graphs. We find that, although much simpler than the codes, the model studied here already displays similar behaviors. We are interested in the van der Waals curve in a regime where the size of each Curie-Weiss model tends to infinity, and the length of the chain and range of the Kac interaction are large but finite. Below the critical temperature, and with appropriate boundary conditions, there appears a series of equilibrium states representing kink-like interfaces between the two equilibrium states of the individual system. The van der Waals curve oscillates periodically around the Maxwell plateau. These oscillations have a period inversely proportional to the chain length and an amplitude exponentially small in the range of the interaction; in other words the spinodal points of the chain model lie exponentially close to the phase transition threshold. The amplitude of the oscillations is closely related to a Peierls-Nabarro free energy barrier for the motion of the kink along the chain. Analogies to similar phenomena and their possible algorithmic significance for graphical models of interest in coding theory and theoretical computer science are pointed out.

show abstract

“…Of course, for J 0 < 0 the ground state of the system has a totally different symmetry with respect to the case J 0 > 0 (compare the asymptotic values toward T = 0 in Figs. (1)(2)(3)(4)(5)(6)(7)), like in the pure model (J = 0), but with the important novelty that now (J > 0) the system is an effective mean-field model with a finite critical temperature.…”

Section: Discussionmentioning

confidence: 99%

“…Traditionally, the concept of the mean-field models is associated with the absence of correlations in the thermodynamic limit. In [1] (see also [2] and [3]) we have shown that this condition is only a sufficient condition for the system to be mean-field, but in general it is not necessary. There are in fact infinite models having non zero correlations but still they are mean-field.…”

Section: Introductionmentioning

confidence: 99%

1D Three-state mean-field Potts model with first- and second-order phase transitions

Ostilli

Mukhamedov

2020

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

We analyze a three-state Potts model built over a ring, with coupling J0, and the fully connected graph, with coupling J. This model is an effective mean-field and can be solved exactly by using transfer-matrix method and Cardano formula. When J and J0 are both positive, the model has a first-order phase transition which turns out to be a smooth modification of the known phase transition of the traditional mean-field Potts model (J > 0 and J0 = 0), despite the connected correlation functions are now non zero. However, when J is positive and J0 negative, besides the first-order transition, there appears also a hidden (non stable) continuous transition. When J is negative the model does not own a phase transition but, interestingly, the dynamics induced by the mean-field equations leads to stable orbits of period 2 with a second-order phase transition and with the classical critical exponent β = 1/2, like in the Ising model.

show abstract

Systems with separable many-particle interactions. II

Cited by 35 publications

References 44 publications

The Ising model in a light-induced quantized transverse field

The Ising model in a light-induced quantized transverse field

Chains of mean-field models

1D Three-state mean-field Potts model with first- and second-order phase transitions

Contact Info

Product

Resources

About