Finite-size scaling study of the equilibrium cluster distribution of the two-dimensional Ising model

Toral, Raúl; Wall, Charles Edward

doi:10.1088/0305-4470/20/14/032

Cited by 12 publications

(8 citation statements)

References 30 publications

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“…These give quantitative ways to characterize the Ising critical point. One finds that µ ≈ 2 and ν death ≈ 1, in agreement with expectations from the distribution of cluster sizes at criticality, which follows a power-law (cluster size) −2.032 [20,21], and the degree of divergence of the spin-spin correlation length, ξ ∼ |T −T c | −1 . It would be interesting to develop this connection to known critical exponents further.…”

Section: Results: Phase Classification and Critical Phenomenasupporting

confidence: 83%

Interpretable Phase Detection and Classification with Persistent Homology

Cole,

Loges,

Shiu

2020

Preprint

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We apply persistent homology to the task of discovering and characterizing phase transitions, using lattice spin models from statistical physics for working examples. Persistence images provide a useful representation of the homological data for conducting statistical tasks. To identify the phase transitions, a simple logistic regression on these images is sufficient for the models we consider, and interpretable order parameters are then read from the weights of the regression. Magnetization, frustration and vortex-antivortex structure are identified as relevant features for characterizing phase transitions.Preprint. Under review.

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Section: Results: Phase Classification and Critical Phenomenasupporting

confidence: 83%

Interpretable Phase Detection and Classification with Persistent Homology

Cole,

Loges,

Shiu

2020

Preprint

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“…However, despite a long history, the local distributions of spins and non-magnetic interacting impurities in the 1D di-lute Ising model have not been described systematically as yet. The size distribution of clusters is of fundamental interest and has been studied intensively in the Ising or similar models [38][39][40][41][42][43][44][45][46][47][48][49][50] .…”

Section: Introductionmentioning

confidence: 99%

Local distributions of the 1D dilute Ising model

Panov

2020

Journal of Magnetism and Magnetic Materials

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The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

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“…Each colour corresponds to an identified cluster. well fitted by a power-law, which might be explained by the reminiscence of the critical behavior of the Ising model in the vicinity of the critical point 37 .…”

Section: Domain Number and Size Distributionmentioning

confidence: 85%

“…In a finite-size system, this leads to an over-abundance of macro-clusters, as thoroughly studied, for example, in Ref. 37 . This increases artificially the contribution of l = 1 in the structure factor S(l), as illustrated in Fig.…”

Section: E Phase Diagram Frontier Expressionsmentioning

confidence: 99%

Domain formation in bicomponent vesicles induced by composition-curvature coupling

Cornet,

Destainville,

Manghi

2020

Preprint

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Lipid vesicles composed of a mixture of two types of lipids are studied by intensive Monte-Carlo numerical simulations. The coupling between the local composition and the membrane shape is induced by two different spontaneous curvatures of the components. We explore the various morphologies of these biphasic vesicles coupled to the observed patterns such as nano-domains or labyrinthine mesophases. The effect of the difference in curvatures, the surface tension and the interaction parameter between components are thoroughly explored. Our numerical results quantitatively agree with previous analytical results obtained by [Gueguen et al., Eur. Phys. J. E, 2014, 37, 76] in the disordered (high temperature) phase. Numerical simulations allow us to explore the full parameter space, especially close to and below the critical temperature, where analytical results are not accessible. Phase diagrams are constructed and domain morphologies are quantitatively studied by computing the structure factor and the domain size distribution. This mechanism likely explains the existence of nano-domains in cell membranes as observed by super-resolution fluorescence microscopy.

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Finite-size scaling study of the equilibrium cluster distribution of the two-dimensional Ising model

Cited by 12 publications

References 30 publications

Interpretable Phase Detection and Classification with Persistent Homology

Interpretable Phase Detection and Classification with Persistent Homology

Local distributions of the 1D dilute Ising model

Domain formation in bicomponent vesicles induced by composition-curvature coupling

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