User:Mwykim7/sandbox

Examples

Ising model and voter dynamics

A 5x5 representational grid of an Ising model. Each space holds some spin value and the red bars indicate communication between neighbors.

Example of social validation in the Sznajd model. If two neighbors agree (top), then their neighbors agree with them. If two neighbors disagree (bottom), their neighbors begin to disagree as well.

One of the most well-known examples in social physics is the relationship of the Ising model and the voting dynamics of a finite population. The Ising model, as a model of ferromagnetism, is represented by a grid of spaces, each of which is occupied by a spin (physics), numerically ±1. Mathematically, the final energy state of the system depends on the interactions of the spaces and their respective spins. For example, if two adjacent spaces share the same spin, the surrounding neighbors will begin to align, and the system will eventually reach a state of consensus. In social physics, it has been observed that voter dynamics in a finite population obey the same mathematical properties of the Ising model. In the social physics model, each spin denotes an opinion, e.g. yes or no, and each space represents a "voter". If two adjacent spaces (voters) share the same spin (opinion), their neighbors begin to align with their spin value; if two adjacent spaces do not share the same spin, then their neighbors remain the same. Eventually, the remaining voters will reach a state of consensus as the "information flows outward".

The Sznajd model is an extension of the Ising model and is classified as an econophysics model. It emphasizes the alignment of the neighboring spins in a phenomenon called "social validation". It follows the same properties as the Ising model and is extended to observe the patterns of opinion dynamics as a whole, rather than focusing on just voter dynamics.

Potts model and cultural dynamics

The Potts model, is a generalization of the Ising model, and has been used to examine the concept of cultural dissemination as described by American political scientist Robert Axelrod. Axelrod's model of cultural dissemination states that individuals who share cultural characteristics are more likely to interact with each other, thus increasing the number of overlapping characteristics and expanding their interaction network. The Potts model has the caveat that each spin can hold multiple values, unlike the Ising model that could only hold one value. Each spin, then, represents an individual's "cultural characteristics... [or] in Axelrod’s words, 'the set of individual attributes that are subject to social influence'". It is observed that, using the mathematical properties of the Potts model, neighbors whose cultural characteristics overlap tend to interact more frequently than with unlike neighbors, thus leading to a self-organizing grouping of similar characteristics. Simulations done on the Potts model both show Axelrod's model of cultural dissemination agrees with the Potts model as an Ising-class model.

Editing "History"

The earliest mentions of a concept of social physics began with the English philosopher Thomas Hobbes. In 1636, Hobbes traveled to Florence, Italy, and met the astronomer Galileo Galilei, of whom was well-known for his contributions to the scieces, namely, the ideas of motion. It was here that Hobbes began to outline the idea of representing the "physical phenomena" of society in terms of motion. In his treatise De Corpore, Hobbes sought to relate the movement of "material bodies" to the mathematical terms of motion outlined by Galileo and similar scientists of the time period. Although there was no explicit mention of "social physics", the sentiment of examing society with scientific methods began before the first written mention of social physics.