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.

Abstract:

We investigate confinement in D = 3 SU(2) lattice gauge theory. We confirm the approximately linear character of confinement at large distances. The corresponding continuum string tension is found to be √σ/g2 = 0.3340 ± 0.0025. We also find that the flux is located within a tube and that the width of this flux tube is l0{reversed tilde equals} 1.22/Tc where Tc is the deconfining temperature. The dominant fluctuations of the confining flux tube appear to be simple wavelike oscillations. This is remarkably similar to the expected properties of confinement in four dimensions. © 1993.