Physics and Mathematics Applications in Social Science

Stauffer, Dietrich; Solomon, Sorin

doi:10.1007/978-0-387-30440-3_408

Cited by 11 publications

(8 citation statements)

References 26 publications

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“…As a next step, let us illustrate how it is applied in social sciences, where an important topic is to understand the social dynamics of a community, e.g. its transition from an initial disordered state to a configuration that displays at least partial order [5,6,[110][111][112][113][114][115]. Inspired by an idea to exploit binarity in social choice, T.C.…”

Section: Simple Model Of Complex Systemsmentioning

confidence: 99%

The fate of Ernst Ising and the fate of his model

Ising¹,

Folk²,

Kenna³

et al. 2017

J. Phys. Stud.

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On this, the occasion of the 20th anniversary of the "Ising Lectures" in Lviv (Ukraine), we give some personal reflections about the famous model that was suggested by Wilhelm Lenz for ferromagnetism in 1920 and solved in one dimension by his PhD student, Ernst Ising, in 1924. That work of Lenz and Ising marked the start of a scientific direction that, over nearly 100 years, delivered extraordinary successes in explaining collective behaviour in a vast variety of systems, both within and beyond the natural sciences. The broadness of the appeal of the Ising model is reflected in the variety of talks presented at the Ising lectures (http://www.icmp.lviv.ua/ising/) over the past two decades but requires that we restrict this report to a small selection of topics. The paper starts with some personal memoirs of Thomas Ising (Ernst's son). We then discuss the history of the model, exact solutions, experimental realisations, and its extension to other fields.

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Section: Simple Model Of Complex Systemsmentioning

confidence: 99%

The fate of Ernst Ising and the fate of his model

Ising¹,

Folk²,

Kenna³

et al. 2017

J. Phys. Stud.

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“…During the last decades there has been considerable progress in describing social systems based on physical notions and mathematical formalism developed in statistical physics and applied mathematics (for a recent review see, e.g., [1,2,3,4,5,6]). In particle, the notion of energy functional (Hamiltonian) and the corresponding master equation were employed to simulate opinion dynamics, the dynamics of culture and languages (e.g., [3,6,7]); the social force model inheriting the basic concepts from Newtonian mechanics was used to simulate traffic flow, pedestrian motion, the motion of bird flocks, fish school, swarms of social insects (e.g., [3,8,9]).…”

Section: Introductionmentioning

confidence: 99%

Dynamical Traps Caused by Fuzzy Rationality as a New Emergence Mechanism

Lubashevsky

2012

Advs. Complex Syst.

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A new emergence mechanism related to the human fuzzy rationality is considered. It assumes that individuals (operators) governing the dynamics of a certain system try to follow an optimal strategy in controlling its motion but fail to do this perfectly because similar strategies are indistinguishable for them. The main attention is focused on the systems where the optimal dynamics implies the stability of a certain equilibrium point in the corresponding phase space. In such systems the fuzzy rationality gives rise to some neighborhood of the equilibrium point, the region of dynamical traps, wherein each point is regarded as an equilibrium one by the operators. So, when the system enters this region and while it is located in it, maybe for a long time, the operator control is suspended. To elucidate a question as to whether the dynamical traps on their own can cause emergent phenomena, the stochastic factors are eliminated from consideration. In this case the system can leave the dynamical trap region only because of the mismatch between actions of different operators. By way of example, a chain of oscillators with dynamical traps is analyzed numerically. As demonstrated, the dynamical traps do induce instability and complex behavior of such systems.

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“…The original IM includes a third parameter known as temperature, denoted as T. However, in numerous non-physics applications of the IM, specifying an equivalent temperature parameter is often challenging. In these cases, the temperature can be understood as representing the willingness or ability of the pattern to deviate from its lowest energy state, potentially accounting for environmental noise [41]. In our study, we assume the temperature to be an unspecified constant that is incorporated into the definitions of J, B and E(ω s ).…”

Section: Model Descriptionmentioning

confidence: 99%

The kinetic Ising model encapsulates essential dynamics of land pattern change

Stepinski,

Nowosad

2023

R. Soc. open sci.

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A land pattern change represents a globally significant trend with implications for the environment, climate and societal well-being. While various methods have been developed to predict land change, our understanding of the underlying change processes remains inadequate. To address this issue, we investigate the suitability of the two-dimensional kinetic Ising model (IM), an idealized model from statistical mechanics, for simulating land change dynamics. We test the IM on a variety of patterns, each with different focus land type. Specifically, we investigate four sites characterized by distinct patterns, presumably driven by different physical processes. Each site is observed on eight occasions between 2001 and 2019. Given the observed pattern at the time t i we find two parameters of the IM such that the model-evolved land pattern at t i +1 resembles the observed land pattern at that time. The data support simulating seven such transitions per site. Our findings indicate that the IM produces approximate matches to the observed patterns in terms of layout, composition, texture and patch size distributions. Notably, the IM simulations even achieve a high degree of cell-scale pattern accuracy in two of the sites. Nevertheless, the IM has certain limitations, including its inability to model linear features, account for the formation of new large patches and handle pattern shifts.

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Physics and Mathematics Applications in Social Science

Cited by 11 publications

References 26 publications

The fate of Ernst Ising and the fate of his model

The fate of Ernst Ising and the fate of his model

Dynamical Traps Caused by Fuzzy Rationality as a New Emergence Mechanism

The kinetic Ising model encapsulates essential dynamics of land pattern change

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