Quantum phase transition for Ising type models on a Cayley tree of order two
In this work, we construct a quantum Markov chain (QMC) associated by the classical Ising model with competing interactions on the Cayley tree of order two. In the construction QMC is defined as a weak limit of finite volume states on quasi-local algebras with boundary conditions. We point out tha...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Conference or Workshop Item |
| Language: | English English |
| Published: |
2014
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/38019/1/Farrukh.pdf http://irep.iium.edu.my/38019/4/ppt_Faruukh.pdf http://irep.iium.edu.my/38019/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this work, we construct a quantum Markov chain (QMC) associated by the classical Ising model
with competing interactions on the Cayley tree of order two. In the construction QMC is defined as a
weak limit of finite volume states on quasi-local algebras with boundary conditions. We point out that
phase transitions in a quantum setting play an important role to understand quantum spin systems
We have defined a notion of phase transition in QMC scheme. Namely, such a notion is based on the
quasi-equivalence of QMC. Therefore, such a phase transition is purely non-commutative. In this work
we establish the existence of the phase transition in the following sense: there exists two quantum
Markov states which are not quasi-equivalent. It turns out that the found critical temperature coincides
with usual critical temperature. |
|---|