# Quantum Ising chains with small-world couplings: No small-world effect at the quantum level; Stability of the quantum critical point

@article{Ostilli2019QuantumIC, title={Quantum Ising chains with small-world couplings: No small-world effect at the quantum level; Stability of the quantum critical point}, author={Massimo Ostilli}, journal={arXiv: Statistical Mechanics}, year={2019} }

Due to the small-world effect, the critical behavior of finite dimensional classical systems of N spins is known to change radically when an O(N) number of couplings are randomly rewired or superimposed onto the original system. In particular, one-dimensional systems acquire a finite critical temperature while two-dimensional systems get higher critical temperatures and, in both cases, the critical behavior turns out to be mean-field like. Here, we prove that at the quantum level the above…

## References

SHOWING 1-10 OF 36 REFERENCES

### Quantum phase transitions

- Physics
- 2001

Abstract We give a general introduction to quantum phase transitions in strongly correlated electron systems. These transitions, which occur at zero temperature when a non-thermal parameter g such as…

### Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information

- Physics
- 2015

The transverse field Ising and XY models (the simplest quantum spin models) provide the organising principle for the rich variety of interconnected subjects which are covered in this book. From a…

### Adiabatic Quantum Computing

- Physics
- 2011

Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems…

### Mean-field and anomalous behavior on a small-world network.

- PhysicsPhysical review letters
- 2003

It is shown that this model enables us, in many cases, to determine the universal critical properties of systems on a small-world network, as well as in the mean-field amplitudes.

### Quantum Computation by Adiabatic Evolution

- Physics
- 2000

We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that…

### Evolution of networks

- Computer Science
- 2002

The recent rapid progress in the statistical physics of evolving networks is reviewed, and how growing networks self-organize into scale-free structures is discussed, and the role of the mechanism of preferential linking is investigated.

### Statistical mechanics methods and phase transitions in optimization problems

- Computer Science, PhysicsTheor. Comput. Sci.
- 2001

### A deceptive step towards quantum speedup detection

- Computer ScienceQuantum Science and Technology
- 2018

These results represent the first steps towards a detection of potential quantum speedup, albeit without a scaling improvement and for synthetic benchmark problems.

### Spin Glasses

- Physics
- 2005

From aphysicalpointofview,spin glasses,asdilutem agneticalloys,arevery interesting system s. They are characterized by such features as exhibiting a new m agnetic phase,where m agnetic m om entsare…

### The One-Dimensional Hubbard Model

- Physics
- 2015

As one of the minimal models for strongly correlated electron systems, the Hubbard model plays a central role in modern condensed matter physics.