arXiv subjects

T. Yukawa

Publications and source records attributed to T. Yukawa.

23 records · Page 2Linked to original sources

arXiv1996

2D Quantum Gravity -Three States of Surfaces-

Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the two-dimensional parameter space are classified into three states: flat, crumpled surface, and branched polymer. In addition, there exists a special point (pure gravity) corresponding to the universal fractal surface. A new probe to detect branched polymers is proposed, which makes use of the minbu(minimum neck baby universe) analysis. This method can clearly distinguish the branched polymer phase from another according to the sizes and arrangements of baby universes. The size distribution of baby universes changes drastically at the transition point between the branched polymer and other kind of surface. The phases of surfaces coupled with multi-Ising spins are studied in a similar manner.

hep-lat↗

arXiv1995

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.

hep-lat↗

arXiv1995

MINBU Distribution of Two Dimensional Quantum Gravity: Simulation Result and Semiclassical Analysis

We analyse MINBU distribution of 2 dimensional quantum gravity. New data of R$^2$-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. The cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing force of $R^2$-term. The dependence on the central charge $c_m$\ and on the $R^2$-coupling are explained for the ordinary 2d quantum gravity and for $R^2$-gravity. The $R^2$-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles . The surface topology is that of a sphere.

hep-th↗

arXiv1995

Finite Size Effects for the Ising Model Coupled to 2-D Random Surfaces

Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by developing an efficient algorithm for recursively solving the quintic equations so encountered. An analytic method for studying finite size effects is developed based on the behaviour of the free energy near its singular points. The generic form of finite size corrections so obtained are seen to be quite different from the phenomenological parameterisations used in the literature. The method of singularities is also applied to study the magnetic susceptibility. A brief discussion is presented on the implications of these results to the problem of a reliable determination of string susceptibility from numerical simulations.

hep-th↗

arXiv1995

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 spins ($m=1$ 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.

hep-th↗