Two-dimensional Dynamical Triangulations Research Articles

Towards elucidation of zero-temperature criticality of the Ising model on 2D dynamical triangulations

We study the zero-temperature criticality of the Ising model on two-dimensional dynamical triangulations to contemplate its physics. As it turns out, an inhomogeneous nature of the system yields an interesting phase diagram and the physics at the zero temperature is quite sensitive about how we cool down the system. We show the existence of a continuous parameter that characterizes the way we approach the zero-temperature critical point and it may enter in a critical exponent.

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

We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the N-by-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.

The complex structure of 2D surfaces

The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex structures for cases when the matter central charges are less than or equal to one, while they become unstable beyond c=1. A natural conjecture that fine planar random network of resistors behave as a continuous sheet of constant resistivity is justified numerically for c<1.

Complex structures defined on dynamically triangulated surfaces

A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as n scalar fields ( n = 0,1 and 4) and m Ising ( m = 1 and 3). We observe a well-defined complex structure for cases when the matter central charges are less than and equal to one, while it becomes unstable beyond c = 1. This can be regarded as the transition expected in analytic theories.