The phase structure of pure Regge gravity

Beirl, W.; Hauke, A.; Homolka, Peter; Krishnan, Balasubramanian; Kröger, H.; Markum, H.; Riedler, J.

doi:10.1016/0920-5632(96)00136-3

Cited by 9 publications

(20 citation statements)

References 11 publications

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“…After this comparative study we turned to the four-dimensional discrete Regge model [6] with spin fields.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…These two β g -values correspond to the two phase transitions of the pure discrete Regge model [6], as shown in Fig. 4.…”

Section: B Ising Spins On a Discrete Regge Modelmentioning

confidence: 99%

“…The transition at positive gravitational coupling of the standard Regge calculus was described in great detail in Ref. [21] and shown to be of first order whereas the transition at negative coupling turned out to be of second order for the discrete Regge model [6]. Together with an eventual second-order transition of the Ising part, the latter one is a candidate for a possible After an initial equilibration time we took about 100 000 measurements for each lattice size.…”

Section: B Ising Spins On a Discrete Regge Modelmentioning

confidence: 99%

“…What happens is that the lattice "freezes" at large positive and negative values of the gravitational coupling, as expected for a spin system [6]. To get more precise ideas about the behavior of the fourdimensional discrete Regge model, we coupled Ising spins to the fluctuating manifolds.…”

Section: Introductionmentioning

confidence: 99%

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Ising spins coupled to a four-dimensional discrete Regge skeleton

2002

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Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.

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“…After this comparative study we turned to the four-dimensional discrete Regge model [6] with spin fields.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…These two β g -values correspond to the two phase transitions of the pure discrete Regge model [6], as shown in Fig. 4.…”

Section: B Ising Spins On a Discrete Regge Modelmentioning

confidence: 99%

Section: B Ising Spins On a Discrete Regge Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ising spins coupled to a four-dimensional discrete Regge skeleton

2002

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“…Then the situation might resemble the more involved fourdimensional case where one has to deal with 10 edges per simplex and the nontrivial EinsteinHilbert action ~-.t~i ~tAt with 50 triangles t per vertex i. Thus the action takes on a large variety of values already for Z2RM and therefore SRC can be approximated more accurately [6]. …”

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confidence: 99%

Standard and Z2-Regge theory in two dimensions

Bittner

Hauke

Holm

et al. 1998

Nuclear Physics B - Proceedings Supplements

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We qualitatively compare two versions of quantum Regge calculus by means of Monte Carlo simulations. In Standard Regge Calculus the quadratic link lengths of the triangulation vary continuously, whereas in the Z2-Regge Model they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z2 model retains the characteristics of standard Regge theory.Standard Regge Calculus (SRC) [1] provides an interesting method to explore quantum gravity in a non-perturbative fashion [2]. Although its code can be efficiently vectorized for large scale computing, it is still a very time demanding enterprise. One therefore seeks for suitable approximations which will simplify the SRC and yet retain most of its universal features. The Z2-Regge Model (Z2RM) [3] could be such a desired simplification. Here the quadratic link lengths of the simplicial complexes are restricted to take on only the two valuesin close analogy to the ancestor of all lattice models, the Ising-Lenz model. To test whether this simpler model is in a reasonable sense still similar to SRC, we study both models in two dimensions and compare a number of observables for one particular lattice size. Starting point for both SRC and Z~.RM is Regge's discrete description of General Relativity [1] in which a given continuum manifold is replaced by a piecewise flat simplicial space. In two dimensions this procedure is easily illustrated by choosing a triangulation of the surface under consideration. Every triangle then represents a part of a piecewise linear manifold. In principle the functional integration should extend over all metrics on all possible topologies, but, as is usually done, we restrict ourselves to one specific topology, the torus, whose Euler characteristic is zero. Consequently the action in the exponent of (2) consists only of a cosmological constant A times the sum over all triangle areas At. Moreover the path-integral approach suffers from a non-uniqueness of the integration measure and it is even claimed that the true measure is of non-local nature [4]. We used as a trial functional integration measure the expression within the square brackets of (2) with m E IR permitting to investigate a 1-parameter family of measures. The function ~" constrains the integration to those Euclidean configurations of link lengths which do not violate the triangle inequalities. In the Z2RM [3] the squared link lengths as well as functions of them are rewritten with respect to (1). Thus the area of a triangle with edges ql, q2, qt is expressed as At = co + Cl(al + ~r2 + az) + c2(~rla2 + 3uO'10"l "~-0"20"/) 71-C30"ldr20r / •The coefficients ci depend on e only and impose the condition e < ~ = e,~,~ in order

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Spins coupled to a Z2-Regge lattice in 4d

Bittner

Janke

Markum

2002

Nuclear Physics B - Proceedings Supplements

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We study an Ising spin system coupled to a fluctuating four-dimensional Z2-Regge lattice and compare with the results of the four-dimensional Ising model on a regular lattice. Particular emphasis is placed on the phase transition of the spin system and the associated critical exponents. We present results from finite-size scaling analyses of extensive Monte Carlo simulations which are consistent with mean-field predictions.

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The phase structure of pure Regge gravity

Cited by 9 publications

References 11 publications

Ising spins coupled to a four-dimensional discrete Regge skeleton

Ising spins coupled to a four-dimensional discrete Regge skeleton

Standard and Z2-Regge theory in two dimensions

Spins coupled to a Z2-Regge lattice in 4d

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