Fixed boundary conditions analysis of the 3d gonihedric Ising model with κ=0

Baig, M.; Clua, J.; Johnston, D.A.; Villanova, Ramon

doi:10.1016/j.physletb.2004.02.002

Cited by 8 publications

(24 citation statements)

References 27 publications

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“…For direct comparison, the resulting quantities are listed in Table 7 after applying all corrections, showing that our data is then in very good agreement with Ref. [9]. For completeness we include here also our data for the magnetic susceptibilityχ.…”

Section: Original Plaquette Model With Fixed Boundary Conditionssupporting

confidence: 76%

“…Direct comparison to Ref. [9] shows that while inverse transition temperatures are reproduced, the extremal values of observables are not. The following observations may help to clarify the deviations.…”

Section: Original Plaquette Model With Fixed Boundary Conditionsmentioning

confidence: 75%

“…The earlier canonical Monte Carlo simulations of the original plaquette model yielded values of β ∞ = 0.50(1) [8] and more recently canonical simulations of the dual model (3) gave β ∞ = 0.510(2) [10]. Another previous estimate for the infinite-lattice inverse transition temperature, reported by Baig et al [9] from canonical simulations using fixed boundary conditions, β ∞ = 0.54757(63), is much closer to the results here.…”

Section: Original Plaquette Model With Periodic Boundary Conditionsmentioning

confidence: 95%

“…that was also used by Baig et al [9], and fitted the inverse temperatures. The statistical errors of the constant a 2 turned out to be of the same order as the value itself, therefore we set a 2 = 0 for the fits in Table 6, intentionally neglecting the contribution O(L −2 ).…”

Section: Original Plaquette Model With Fixed Boundary Conditionsmentioning

confidence: 99%

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Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

2014

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The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of β ∞ = 0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension σ = 0.12037(18), using the statistics of suppressed configurations.

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Section: Original Plaquette Model With Fixed Boundary Conditionssupporting

confidence: 76%

Section: Original Plaquette Model With Fixed Boundary Conditionsmentioning

confidence: 75%

Section: Original Plaquette Model With Periodic Boundary Conditionsmentioning

confidence: 95%

Section: Original Plaquette Model With Fixed Boundary Conditionsmentioning

confidence: 99%

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Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

2014

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“…model with fixed boundary conditions have given good agreement with this scaling [17]. The approach taken to enumerating the ground states by splitting the lattice into elementary cubes can also be applied to mean field theory for the model and to extensions of mean field theory such as the cluster variational method.…”

Section: Equilibrium Behaviour By Various Meansmentioning

confidence: 71%

The Gonihedric Ising Model and Glassiness

Johnston

Lipowski

Malmini

Rugged Free Energy Landscapes

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(Pre-)History of the ModelThe Gonihedric 3D Ising model is a lattice spin model in which planar Peierls boundaries between + and − spins can be created at zero energy cost. Instead of weighting the area of Peierls boundaries as the case for the usual 3D Ising model with nearest neighbour interactions, the edges, or "bends" in an interface are weighted, a concept which is related to the intrinsic curvature of the boundaries in the continuum.The model is a generalised Ising model living on a cubic 3D lattice with nearest neighbour, next to nearest-neighbour and plaquette interactions. The ratio between the couplings of these three terms is fixed to a one parameter family which endows the model with unusual properties both in and out of equilibrium. Of particular interest for the discussion here will be that the model manifests all the indications of glassy behaviour without any recourse to quenched disorder, whilst still possessing a crystalline low temperature phase in equilibrium.In these notes we follow a roughly chronological order by first reviewing the background to the formulation of the model, before moving on to the elucidation of the equilibrium phase diagram by various means and then to the investigation of the non-equilibrium, glassy behaviour of the model. We apologize in advance for our narrow focus on things Gonihedric at the expense of other lattice models with glassy behaviour, since the aim is to concentrate on giving an overview of the Gonihedric Ising model in 3D.The model has an unusual genesis since it was originally introduced as a potential discretization of string theory. The Nambu-Goto [1] action (or Hamiltonian in statistical mechanical language) in bosonic string theory is given by the area swept out by the string worldsheet as it moves through spacetime. Directly discretizing euclideanized versions of this action produced ensembles of surfaces, i.e. string worldsheets, which were dominated by collapsed and irregular configurations such as that in Fig.1 and which were unsuitable for

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The dual gonihedric 3D Ising model

Johnston

Ranasinghe

2011

J. Phys. A: Math. Theor.

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We investigate the dual of the κ = 0 gonihedric Ising model on a 3D cubic lattice, which may be written as an anisotropically coupled Ashkin–Teller model. The original κ = 0 gonihedric model has a purely plaquette interaction, displays a first order transition and possesses a highly degenerate ground state. We find that the dual model admits a similar large ground state degeneracy as a result of the anisotropic couplings and investigate the coupled mean-field equations for the model on a single cube. We also carry out Monte Carlo simulations which confirm a first order phase transition in the model and suggest that the ground state degeneracy persists throughout the low temperature phase. Some exploratory cooling simulations also hint at non-trivial dynamical behaviour.

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Fixed boundary conditions analysis of the 3d gonihedric Ising model with κ=0

Cited by 8 publications

References 27 publications

Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

The Gonihedric Ising Model and Glassiness

The dual gonihedric 3D Ising model

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