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Ising is Everywhere (in Science and in 91̽��)

Just over 100 years ago, Ernst Ising solved a simple model for a one-dimensional ferromagnet in his PhD thesis. In the century since, the Ising model has come become one of the best-studied models in physics: a conservative estimate is that nearly a quarter of a million papers discuss it or its variants, in fields ranging from statistical mechanics to lattice gauge theory, and from neural networks to social dynamics. 

In this series of three lectures, Profs. Siddharth Parameswaran, Fabian Essler, and Paul Fendley will attempt to convey some idea of why the model continues to fascinate physicists to this day, illustrate how it informs our ideas about quantum phases of matter, and sketch some of the beautiful mathematical ideas that underpin its exact solution in two dimensions. Along the way, they will highlight the role it has played in the work of physicists associated with the RPC, from Rudolf Peierls and Roger Elliott to David Sherrington and John Cardy.

Lecture 1: 'The Ising Model: What, Why, and Where?' (Prof Sid Parameswaran)

I will give an introduction to the Ising model, starting with its historical beginnings as a model of magnetism just over a century ago (the what). I will explain how the work of Rudolf Peierls and others made it the paradigmatic model for studying phase transitions (the why) before surveying some of the many different guises in which the model appears and giving an account of the surprising range of physical problems it has inspired or informed (the where).

Lecture 2: 'The Ising Model in the 21st Century' (Prof Fabian Essler)

The Ising model continues to play an important role in present-day research. I will discuss some recent applications to confinement in quasi-one-dimensional magnetic insulators and non-equilibrium quantum dynamics.

Lecture 3: 'From Ising to Quantum Deconfinement' (Prof Paul Fendley)

The two-dimensional Ising model is ubiquitous in theoretical physics. One reason is that many of its properties can be computed exactly by using some clever tricks. One such trick is to exploit its relation to counting “dimer” configurations, such as finding the number of different ways of placing 32 dominoes on a chessboard. I will describe this method (and give this number). I also will explain how solving this counting problem allows one to find a quantum model exhibiting deconfinement, where the seemingly fundamental particles of a system turn out to be composites.

Recordings of all talks will be made available on this page in the weeks following the event.