Noncanonical path and surface simulation

Baumann, Bernd

doi:10.1016/0550-3213(87)90346-4

Cited by 35 publications

(29 citation statements)

References 13 publications

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“…A figure corresponding to (27) and (28) looks similar to figure 2, but is not very instructive as all three fits lines are almost on top of one another.…”

Section: Three Dimensional Edwards-anderson Ising Spin Glasssupporting

confidence: 49%

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Multicanonical recursions

Berg

1996

J Stat Phys

101

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“…A figure corresponding to (27) and (28) looks similar to figure 2, but is not very instructive as all three fits lines are almost on top of one another.…”

Section: Three Dimensional Edwards-anderson Ising Spin Glasssupporting

confidence: 49%

“…Here β(E), α(E) is the multicanonical parameterization [1,2,27]. Its rationale is to relate to the temperature.…”

Section: Multicanonical Samplingmentioning

confidence: 99%

Multicanonical recursions

Berg

1996

J Stat Phys

101

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“…Since we are forced to use a grand canonical updating where the volume of the universe N 4 is changing, it is convenient to use the technique first introduced in [30] and used successfully in the simulations in three-dimensional gravity [24,27]. It allows us to get as close to a canonical simulation as possible and it provides at the same time an estimate of the critical point κ c 4 (κ 2 ) for a given value of the coupling constant κ 2 .…”

Section: The Numerical Methodsmentioning

confidence: 99%

Quantum gravity, dynamical triangulations and higher-derivative regularization

Ambjørn¹,

Jurkiewicz

Kristjansen³

1993

Nuclear Physics B

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We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the EinsteinHilbert action plus an R 2 -term. The phase diagram as a function of the bare coupling constants is studied in the search for a sensible continuum limit. For small values of the coupling constant of the R 2 term the model seems to belong to the same universality class as the model with pure Einstein-Hilbert action and exhibits the same phase transition. The order of the transition may be second or higher. The average curvature is positive at the phase transition, which makes it difficult to understand the possible scaling relations of the model.

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“…In accordance with detailed balance, standard Metropolis and heat bath updating algorithms have been generalized to the multicanonical situation [3,9]. Finally we obtain the canonical action density distribution P L (S) through a reweighting step similar to [10,11] from the multicanonical distribution P L (S):…”

mentioning

confidence: 99%

Multicanonical ensemble: A new approach to simulate first-order phase transitions

1992

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Abstract:Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes 100 × 100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to L 2.65 . Thus the computational effort as counted per degree of freedom for generating an independent configuration in the unstable region of the model rises proportional to V 2.3 , where V is the volume of the system. On our largest lattice we gain more than two orders of magnitude as compared to a standard heat bath algorithm. As a first physical application we report a high precision computation of the interfacial tension.

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Noncanonical path and surface simulation

Cited by 35 publications

References 13 publications

Multicanonical recursions

Multicanonical recursions

Quantum gravity, dynamical triangulations and higher-derivative regularization

Multicanonical ensemble: A new approach to simulate first-order phase transitions

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