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2192 results in Statistical Physics

Page 31 of 110

  • 10 - Phase Transitions and Order

  • Malcolm P. Kennett, Simon Fraser University, British Columbia
  • Book:
    Essential Statistical Physics
    Published online:
    29 August 2020
    Print publication:
    16 July 2020, pp 190-221

  • Summary

    Many different phases of matter can be characterized by the symmetries that they break.The Ising model for interacting spins illustrates this idea.In the absence of a magnetic field, there is a critical temperature, below which there is ferromagnetic ordering, and above which there is not.The magnetization is the order parameter for this transition: it is non-zero only when there is ferromagnetic ordering.The ferromagnetic phase transition in the Ising model is explored using the approximate method of mean field theory.Exact solutions are known for the Ising model in one and two dimensions and are discussed, along with numerical solutions using Monte Carlo simulations.Finally, the ideas of broken symmetry and their relationship to phase transitions are placed in the general framework of Landau theory and compared to results from mean field theory.

A First Course in Network Science
  • Filippo Menczer, Santo Fortunato, Clayton A. Davis
  • Published online:
    05 February 2020
    Print publication:
    23 January 2020
  • Networks are everywhere: networks of friends, transportation networks and the Web. Neurons in our brains and proteins within our bodies form networks that determine our intelligence and survival. This modern, accessible textbook introduces the basics of network science for a wide range of job sectors from management to marketing, from biology to engineering, and from neuroscience to the social sciences. Students will develop important, practical skills and learn to write code for using networks in their areas of interest - even as they are just learning to program with Python. Extensive sets of tutorials and homework problems provide plenty of hands-on practice and longer programming tutorials online further enhance students' programming skills. This intuitive and direct approach makes the book ideal for a first course, aimed at a wide audience without a strong background in mathematics or computing but with a desire to learn the fundamentals and applications of network science.

Thermal Physics
  • Energy and Entropy
  • David Goodstein
  • Published online:
    28 May 2018
    Print publication:
    19 February 2015
  • Written by distinguished physics educator David Goodstein, this fresh introduction to thermodynamics, statistical mechanics, and the study of matter is ideal for undergraduate courses. The textbook looks at the behavior of thermodynamic variables and examines partial derivatives - the essential language of thermodynamics. It also explores states of matter and the phase transitions between them, the ideal gas equation, and the behavior of the atmosphere. The origin and meaning of the laws of thermodynamics are then discussed, together with Carnot engines and refrigerators, and the notion of reversibility. Later chapters cover the partition function, the density of states, and energy functions, as well as more advanced topics such as the interactions between particles and equations for the states of gases of varying densities. Favoring intuitive and qualitative descriptions over exhaustive mathematical derivations, the textbook uses numerous problems and worked examples to help readers get to grips with the subject.

Page 31 of 110