Ising spins on discrete Regge lattices

Bittner, Elmar; Janke, Wolfhard; Markum, H.; Riedler, J.

doi:10.1016/s0378-4371(99)00487-2

Cited by 4 publications

(7 citation statements)

References 21 publications

(27 reference statements)

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“…is defined as in two dimensions [2], with the barycentric area A ij associated with a link l ij , A ij = t ⊃ lij 1 3 A t . We chose the simple uniform measure as in the pure gravity simulations [1], D[q] = l dq l F (q l ).…”

Section: Model and Observablesmentioning

confidence: 99%

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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Section: Model and Observablesmentioning

confidence: 99%

Spins coupled to a Z2-Regge lattice in 4d

Bittner

Janke

Markum

2002

Nuclear Physics B - Proceedings Supplements

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“…11 shows the expectation value of the area A s given by eq. (3.1) against β for N = 2 21 , µ = 0.3, K s = 100, K t = 50 and D = 30. As clearly seen in the figure, the numerical results nicely reproduce the exact value A s = β + 3/2, presented in eq.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Fig. 13 shows the relative error of A s defined by ∆A = |1 − A s /(β + 3/2)| against K s , K t and D for β = 0 (Left) and β = 1 (Right) at N = 2 21 and µ = 0.3. The accuracy is improved by increasing K s , K t and D. These results show that the TRG calculation works well for the analytically continued 2d Lorentzian QRC.…”

Section: Numerical Resultsmentioning

confidence: 99%

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Tensor network approach to 2d Lorentzian quantum Regge calculus

Ito¹,

Kadoh²,

Yuki³

2022

Preprint

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We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity.

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“…is defined as in two dimensions [8][9][10], with the barycentric area A ij associated with a link l ij ,…”

Section: Models and Observablesmentioning

confidence: 99%

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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Ising spins on discrete Regge lattices

Cited by 4 publications

References 21 publications

Spins coupled to a Z2-Regge lattice in 4d

Spins coupled to a Z2-Regge lattice in 4d

Tensor network approach to 2d Lorentzian quantum Regge calculus

Ising spins coupled to a four-dimensional discrete Regge skeleton

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