Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations

Abstract

We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the $N\times N$ hermitian two-matrix model with the introduction of a loop-counting parameter and linear terms in the potential. We show that in the large-N limit even though the Ising model is classical, the critical temperature can reach absolute zero by tuning the loop-counting parameter, and the corresponding continuum theory turns out to be the quantised theory of neither pure gravity nor gravity coupled to conformal matter with central charge being 1/2.

25 pages, 3 figures; v4: minor corrections

References in corpus (16)

• Nonperturbative Quantum Gravity
• A new perspective on matter coupling in 2d quantum gravity
• 2d CDT is 2d Horava-Lifshitz quantum gravity
• A String Field Theory based on Causal Dynamical Triangulations
• Integrable 2D Lorentzian Gravity and Random Walks
• On the spectral dimension of causal triangulations
• A new continuum limit of matrix models
• Crossing the c=1 barrier in 2d Lorentzian quantum gravity
• Putting a cap on causality violations in CDT
• Trees and spatial topology change in CDT
• New multicritical matrix models and multicritical 2d CDT
• An Analytical Analysis of CDT Coupled to Dimer-like Matter
• On the Quantum Geometry of Multi-critical CDT
• Causal Dynamical Triangulation with Extended Interactions in 1+1 Dimensions
• A restricted dimer model on a 2-dimensional random causal triangulation
• Scale-dependent Hausdorff dimensions in 2d gravity

Cited by in corpus (2)

• Towards elucidation of zero-temperature criticality of Ising model on 2d DT
• Branched polymers with loops coupled to the critical Ising model