Particle theory

Abstract:

We perform finite temperature simulations of SU (2) lattice gauge fields in two spatial dimensions. We calculate the correlation length and find that it appears to diverge at a critical temperature, indicating a second order phase transition. Our average value for the associated critical exponent is γ = 0.975+0.045-0.035 which is consistent with the value γ = 1 in the D = 2 Ising model. We calculate the critical temperature, Tc, in units of the string tension, σ, and extrapolate to the continuum limit. If we use the theoretically favoured value, γ = 1, in our fits for Tc then we obtain Tc σ = 1.121 ± 0.008. If, instead, we allow γ tobe free then we obtain a somewhat less precise value: Tc σ = 1.118+0.034-0.016. We note that while this value is very different from the corresponding value in four dimensions, most of the difference can be understood on simple dimensional grounds. © 1993.

Abstract:

We consider methods of interpolating between the crystalline and dynamically triangulated random surface models. We argue that actions based on the deviation from six of the coordination number at a site are inadequate and propose an alternative based on Alexander moves. Two simplified models, one of which has a phase transition and the other of which does not, are discussed.