Smeared phase transition in a three-dimensional Ising model with planar defects: Monte Carlo simulations

Sknepnek, Rastko; Vojta, Thomas

doi:10.1103/physrevb.69.174410

Cited by 37 publications

(53 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This has indeed been observed not just in the famous McCoy-Wu model [61,62,63] or in the layered classical Ising model [79] discussed in Sec. 5.1, but also in randomly layered Heisenberg [115,116] and XY [117] models.…”

Section: Discussionmentioning

confidence: 79%

See 1 more Smart Citation

Phases and phase transitions in disordered quantum systems

Vojta

2013

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase transitions. We then derive criteria governing under what conditions spatial disorder or randomness can change the properties of a phase transition. After introducing the strong-disorder renormalization group method, we discuss in detail some of the exotic phenomena arising at phase transitions in disordered quantum systems. These include infinite-randomness criticality, rare regions and quantum Griffiths singularities, as well as the smearing of phase transitions. We also present a number of experimental examples.Comment: Pedagogical introduction to strong disorder physics at quantum phase transitions. Based on lectures given at the XVII Training Course in the Physics of Strongly Correlated Systems in Vietri sul Mare, Italy in October 2012. Submitted to the proceedings of this school. 60 pages and 23 figures. Builds on material reviewed in arXiv:cond-mat/0602312 and arXiv:1005.270

show abstract

Section: Discussionmentioning

confidence: 79%

“…The interaction J i at the corresponding position is indicated in the lower panel (after Ref. [79]). magnetization tail behaves exponentially at intermediate p but vanishes as a power-law for p → 1 [80,81].…”

Section: Optimal Fluctuation Theorymentioning

confidence: 99%

Phases and phase transitions in disordered quantum systems

Vojta

2013

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another possible explanation is that we are dealing with smeared phase transitions. One classic example is that of the Ising model in systems with defects [8]. The Ising model considers spins, which can take a +1 or −1 value, laying on the nodes of a regular lattice.…”

Section: A Empirical Resultsmentioning

confidence: 99%

Smeared phase transitions in percolation on real complex networks

Allard

2019

Phys. Rev. Research

View full text Add to dashboard Cite

Percolation on complex networks is used both as a model for dynamics on networks, such as network robustness or epidemic spreading, and as a benchmark for our models of networks, where our ability to predict percolation measures our ability to describe the networks themselves. In many applications, correctly identifying the phase transition of percolation on real-world networks is of critical importance. Unfortunately, this phase transition is obfuscated by the finite size of real systems, making it hard to distinguish finite size effects from the inaccuracy of a given approach that fails to capture important structural features. Here, we borrow the perspective of smeared phase transitions and argue that many observed discrepancies are due to the complex structure of real networks rather than to finite size effects only. In fact, several real networks often used as benchmarks feature a smeared phase transition where inhomogeneities in the topological distribution of the order parameter do not vanish in the thermodynamic limit. We find that these smeared transitions are sometimes better described as sequential phase transitions within correlated subsystems. Our results shed light not only on the nature of the percolation transition in complex systems, but also provide two important insights on the numerical and analytical tools we use to study them. First, we propose a measure of local susceptibility to better detect both clean and smeared phase transitions by looking at the topological variability of the order parameter. Second, we highlight a shortcoming in state-of-the-art analytical approaches such as message passing, which can detect smeared transitions but not characterize their nature.

show abstract

“…This argument suggests that the phenomenology of the transition can completely change, if the system permits rare regions that can undergo a true phase transition independently of the bulk, leading to a static order parameter on the rare regions. It was recently found [5,[31][32][33] that this does indeed happen, and that it leads to a smeared global phase transition.…”

Section: Smearing Mechanismmentioning

confidence: 96%

“…Since a 2D Ising model has an ordered phase, each rare region can independently undergo the magnetic phase transition. This leads to a smeared global phase transition in the 3D Ising model with planar defects [31,32]…”

Section: Classical Magnets With Extended Defectsmentioning

confidence: 99%

Critical points and quenched disorder: From Harris criterion to rare regions and smearing

Vojta

Sknepnek

2004

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system.

show abstract

Smeared phase transition in a three-dimensional Ising model with planar defects: Monte Carlo simulations

Cited by 37 publications

References 47 publications

Phases and phase transitions in disordered quantum systems

Phases and phase transitions in disordered quantum systems

Smeared phase transitions in percolation on real complex networks

Critical points and quenched disorder: From Harris criterion to rare regions and smearing

Contact Info

Product

Resources

About