Non-trivial lattice random surfaces

Baumann, Bernd; Berg, Bernd A.

doi:10.1016/0370-2693(85)90046-2

Cited by 32 publications

(17 citation statements)

References 13 publications

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“…Configurations with the multicanonical probability P ′ B are generated with a generalized Metropolis or heat bath updating procedure. The original distribution (Baumann and Berg, 1985;Swendsen, 1988 and.…”

Section: Multicanonical Algorithmsmentioning

confidence: 99%

Phase transitions in quantum chromodynamics

1996

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The current understanding of finite temperature phase transitions in QCD is reviewed. A critical discussion of refined phase transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out, where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations which assume thermodynamic equilibrium. Promising new approaches to implement nonequilibrium aspects in the thermodynamics of heavy-ion collisions are described.

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Section: Multicanonical Algorithmsmentioning

confidence: 99%

Phase transitions in quantum chromodynamics

1996

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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):…”

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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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“…It is interesting, as pointed out in [4], that this value of γ has been seen in simulations of a random surface in a three dimensional hypercubic lattice with a weak self-avoidance condition [10].We have, however, not been able to see any relation between that model and the one studied here.…”

Section: Discussionmentioning

confidence: 53%

“…which have the same structure as (7), (9), (10). Random surface models with these generalized matter fields have not been explicitly solved so G(μ,κ) is not known; however we see that such models which belong to the minimal series withγ = −1/n with n = 2, 3, 4, .…”

Section: Discussionmentioning

confidence: 99%

The phase diagram of an Ising model on a polymerized random surface

Jónsson

Wheater

1995

Physics Letters B

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Abstract. We construct a random surface model with a string susceptibility exponent γ = 1/4 by taking an Ising model on a random surface and introducing an additional degree of freedom which amounts to allowing certain outgrowths on the surfaces. Fine tuning the Ising temperature and the weight factor for outgrowths we find a triple point where γ = 1/4. At this point magnetized and nonmagnetized gravity phases meet a branched polymer phase.

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Non-trivial lattice random surfaces

Cited by 32 publications

References 13 publications

Phase transitions in quantum chromodynamics

Phase transitions in quantum chromodynamics

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

The phase diagram of an Ising model on a polymerized random surface

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