Random network models and quantum phase transitions in two dimensions

Quantum phase transitions of correlated electrons in two dimensions

We review the theories of a few quantum phase transitions in two-dimensional correlated electron systems and discuss their application to the cuprate high temperature superconductors. The coupled-ladder antiferromagnet displays a transition between the Néel state and a spin gap paramagnet with a sharp S = 1 exciton: we develop a careful argument which eventually establishes that this transition...

Quantum Phase Transitions in Random Systems

Phase transitions and random quantum satisfiability

Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA1-complete quantum satisfiability (QSAT) problem introduced by Bravyi [1]. QSAT appropriately generalizes the NP-complete classical satisfiability (SAT) problem. We show ...

Site Percolation and Phase Transitions in Two Dimensions

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters undergo a percolation transition exactly at the critical point. We show that this result is quite general in two dimensions for models undergoing a continuous ...

Heterotic Strings in Two Dimensions and New Stringy Phase Transitions

We discuss heterotic string theories in two dimensions with gauge groups Spin(24) and Spin(8) × E8. After compactification the theories exhibit a rich spectrum of states with both winding and momentum. At special points some of these stringy states become massless, leading to new first order phase transitions. For example, the thermal theories exhibit standard thermodynamics below the phase tra...