Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-06-21
Annals Phys. 273 (1999) 72-98
Physics
High Energy Physics
High Energy Physics - Theory
25 pages Plain TeX
Scientific paper
10.1006/aphy.1998.5868
We give a lattice theory treatment of certain one and two dimensional quantum field theories. In one dimension we construct a combinatorial version of a non-trivial field theory on the circle which is of some independent interest in itself while in two dimensions we consider a field theory on a toroidal triangular lattice. We take a continuous spin Gaussian model on a toroidal triangular lattice with periods $L_0$ and $L_1$ where the spins carry a representation of the fundamental group of the torus labeled by phases $u_0$ and $u_1$. We compute the {\it exact finite size and lattice corrections}, to the partition function $Z$, for arbitrary mass $m$ and phases $u_i$. Summing $Z^{-1/2}$ over a specified set of phases gives the corresponding result for the Ising model on a torus. An interesting property of the model is that the limits $m\rightarrow0$ and $u_i\rightarrow0$ do not commute. Also when $m=0$ the model exhibits a {\it vortex critical phase} when at least one of the $u_i$ is non-zero. In the continuum or scaling limit, for arbitrary $m$, the finite size corrections to $-\ln Z$ are {\it modular invariant} and for the critical phase are given by elliptic theta functions. In the cylinder limit $L_1\rightarrow\infty$ the ``cylinder charge'' $c(u_0,m^2L_0^2)$ is a non-monotonic function of $m$ that ranges from $2(1+6u_0(u_0-1))$ for $m=0$ to zero for $m\rightarrow\infty$ but from which one can determine the central charge $c$. The study of the continuum limit of these field theories provides a kind of quantum theoretic analog of the link between certain combinatorial and analytic topological quantities.
Connor Denjoe O'
Nash Charles
No associations
LandOfFree
Modular invariance, lattice field theories and finite size corrections does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Modular invariance, lattice field theories and finite size corrections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modular invariance, lattice field theories and finite size corrections will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-66898