X iv : c on d - m at / 9 60 41 18 v 2 1 7 A pr 1 99 6 Entangled Polymer Rings in 2 D and Confinement

ar X iv : c on d - m at / 9 60 41 18 v 1 1 6 A pr 1 99 6 Entangled Polymer Rings in 2 D and Confinement

The statistical mechanics of polymer loops entangled in the two-dimensional array of randomly distributed obstacles of infinite length is discussed. The area of the loop projected to the plane perpendicular to the obstacles is used as a collective variable in order to re-express a (mean field) effective theory for the polymer conformation.

ar X iv : h ep - t h / 97 03 03 6 v 2 2 9 A pr 1 99 7 1 M - Theory , Torons and Confinement

We study the decompactification limit of M-theory superpotentials for N = 1 four dimensional supersymmetric gauge theories. These superpotentials can be interpreted as generated by toron configurations. The connection with the confinement picture in the maximal abelian gauge is discussed. Polyakov's compact electrodynamics in three dimensions [1] constitutes a pardigmatic model for electric con...

ar X iv : 0 90 7 . 41 78 v 1 [ m at h . PR ] 2 3 Ju l 2 00 9 An Introduction to Stochastic PDEs

2 Some Motivating Examples 2 2.1 A model for a random string (polymer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 The stochastic Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The stochastic heat equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 What have we learned? . . . . . . . . . . . . . . . . . . . . . ...

ar X iv : c on d - m at / 9 60 31 90 v 1 2 9 M ar 1 99 6 The Four - Dimensional XY Spin Glass

ar X iv : c on d - m at / 9 60 31 41 v 1 2 1 M ar 1 99 6 March 1996 A remark on off - diagonal long - range order

In this work, we study some general property of a strongly correlated electron system defined on a lattice. Assuming that the lattice system exhibits off-diagonal long-range order, we show rigorously that this assumption would lead to Meissner effect. This generalizes previous results of continuous case to a lattice electron system.