The random field Blume-Capel model revisited

Santos, P. V.; Costa, F. A. da; Araújo, João M. de

doi:10.1016/j.jmmm.2017.12.008

Cited by 20 publications

(16 citation statements)

References 46 publications

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“…It would be interesting to see if a one parameter Landau theory can be built, which has a BEP as seen in the strong disorder case in our work. A study of three fields diagram for random field Blume Capel model would also be useful to understand the nature of TCPs reported [44] in the (T, ∆) phase diagram [45].…”

Section: Discussionmentioning

confidence: 99%

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Sumedha

Mukherjee

2020

Phys. Rev. E

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We obtain the phase diagram for the Blume-Capel model with bimodal distribution for random crystal fields, in the space of three fields: temperature(T ), crystal field(∆) and magnetic field (H). We find that three critical lines meet at a tricritical point, but only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first order surface in the H = 0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.

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Section: Discussionmentioning

confidence: 99%

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Sumedha

Mukherjee

2020

Phys. Rev. E

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“…The pure system features a tricritical point separating second-order and first-order lines of transi- tions [51]. There are many open questions concerning the behavior of this model in presence of quenched disorder, be it of random-bond type as considered here or in the form of random (crystal) fields [52,53]. In particular, conflicting results have been found for the universality class of the ex-first-order segment of the transition line [54], and some authors have favored a scenario that contradicts universality [55,56].…”

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confidence: 99%

Universality from disorder in the random-bond Blume-Capel model

et al. 2018

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Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L^{*}≈32 for the chosen parameters.

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“…The triads can be in 10 different states σ ∈ {A, B, C, D, E, F, G, H, I, J} and the Hamiltonian (2) determines the corresponding energies E σ (see table 1 and figure 2). The Hamiltonian (2) bears resemblance with the one from the Blume-Capel model [30,31,32,33], with the addition of a three-edge interaction related to standard social balance. The corresponding strength parameter α is anticipated to be positive.…”

Section: Associated Energymentioning

confidence: 99%

Social stability and extended social balance—Quantifying the role of inactive links in social networks

Belaza¹,

Ryckebusch²,

Bramson³

et al. 2019

Physica A: Statistical Mechanics and its Applications

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Structural balance in social network theory starts from signed networks with active relationships (friendly or hostile) to establish a hierarchy between four different types of triadic relationships. The lack of an active link also provides information about the network. To exploit the information that remains uncovered by structural balance, we introduce the inactive relationship that accounts for both neutral and nonexistent ties between two agents. This addition results in ten types of triads, with the advantage that the network analysis can be done with complete networks. To each type of triadic relationship, we assign an energy that is a measure for its average occupation probability. Finite temperatures account for a persistent form of disorder in the formation of the triadic relationships. We propose a Hamiltonian with three interaction terms and a chemical potential (capturing the cost of edge activation) as an underlying model for the triadic energy levels. Our model is suitable for empirical analysis of political networks and allows to uncover generative mechanisms. It is tested on an extended data set for the standings between two classes of alliances in a massively multi-player on-line game (MMOG) and on real-world data for the relationships between countries during the Cold War era. We find emergent properties in the triadic relationships between the nodes in a political network. For example, we observe a persistent hierarchy between the ten triadic energy levels across time and networks. In addition, the analysis reveals consistency in the extracted model parameters and a universal data collapse of a derived combination of global properties of the networks. We illustrate that the model has predictive power for the transition probabilities between the different triadic states. arXiv:1807.09042v3 [physics.soc-ph] 17 Dec 2018Heider [1] and its extension to graphs by Cartwright [2] is based on active relationships that can be friendly ("+") or unfriendly ("−"). The four types of emerging triadic relationships are categorized in two stable (= balanced) and two unstable (= unbalanced) ones, whereby one anticipates an overall tendency to create more balanced triads. Balanced triads [+ + +] and [+ − −] have an even number of "−" edges. Unbalanced [+ + −] and [− − −] triads, however, are a key ingredient in real-life political networks. Balance theory has found applications in many branches of sciences including psychology [1], studies of international networks [3,4,5,6,7], sociology [8,9,10,11,12] and ecology [13].As balance theory introduces correlations between the edge attributes in triads, in a physics framework [14,15,16,17] it maps onto a system with predominant three-edge interactions. Associating the existence of unbalanced triads to the occurrence of a non-vanishing excitation energy, the principles of social balance can be mapped onto a model with variations in an energy landscape. Marvel et al. [14] investigated the energy landscape of a social-balance inspired system and stressed the occurrence ...

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The random field Blume-Capel model revisited

Cited by 20 publications

References 46 publications

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Emergence of a bicritical end point in the random-crystal-field Blume-Capel model

Universality from disorder in the random-bond Blume-Capel model

Social stability and extended social balance—Quantifying the role of inactive links in social networks

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