A restricted dimer model on a two-dimensional random causal triangulation

TY - JOUR

T1 - A restricted dimer model on a two-dimensional random causal triangulation

AU - Ambjørn, Jan

AU - Durhuus, Bergfinnur

AU - Wheater, J. F.

PY - 2014/9/12

Y1 - 2014/9/12

N2 - We introduce a restricted hard dimer model on a random causal triangulation that is exactly solvable and generalizes a model recently proposed by Atkin and Zohren (2012 Phys. Lett. B 712 445-50). We show that the latter model exhibits unusual behaviour at its multicritical point; in particular, its Hausdorff dimension equals 3 and not as would be expected from general scaling arguments. When viewed as a special case of the generalized model introduced here we show that this behaviour is not generic and therefore is not likely to represent the true behaviour of the full dimer model on a random causal triangulation.

AB - We introduce a restricted hard dimer model on a random causal triangulation that is exactly solvable and generalizes a model recently proposed by Atkin and Zohren (2012 Phys. Lett. B 712 445-50). We show that the latter model exhibits unusual behaviour at its multicritical point; in particular, its Hausdorff dimension equals 3 and not as would be expected from general scaling arguments. When viewed as a special case of the generalized model introduced here we show that this behaviour is not generic and therefore is not likely to represent the true behaviour of the full dimer model on a random causal triangulation.

U2 - 10.1088/1751-8113/47/36/365001

DO - 10.1088/1751-8113/47/36/365001

M3 - Journal article

SN - 1751-8113

VL - 47

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

M1 - 365001

ER -