Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2003-12-23
Physics
Condensed Matter
Disordered Systems and Neural Networks
25 pages, 7 figures, Published in "Quantum Annealing and Related Optimization Methods", A. Das and B. K. Chakrabarti (Eds.), L
Scientific paper
We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Next we introduce Suzuki-Trotter formalism to show the correspondence between $d$-dimensional quantum system with a $(d+1)$-dimensional classical system. We then discuss transverse Ising spin glass models, namely S-K model, E-A model, and the $\pm J$ model with Ising spin in transverse field. We briefly discuss the mean field, exact diagonalization, and quantum Monte Carlo results for their phase diagrams. Next we discuss the question of replica symmetry restoration in quantum spin glasses (due to tunnelling possibility through the barriers). Then we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses. We have also breifly discussed the possibility of Quantum Annealing in context of kinetically constrained systems. Mean-field calculation for BCS superconductivity, Real-space RG calculation for one dimensional transverse Ising system, scattering amplitude calculation for tunneling through asymmetric barrier (useful for quantum kinetically constrained system) are given in the appendices.
Chakrabarti Bikas K.
Das Arnab
No associations
LandOfFree
Tranverse Ising Model, Glass and Quantum Annealing 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 Tranverse Ising Model, Glass and Quantum Annealing, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tranverse Ising Model, Glass and Quantum Annealing will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-322997