Barry Simon is a mathematical physicist who has served on the faculty of Princeton and Caltech. Noted for his many books and research contributions, his honours include the AMS Steele Prize for Lifetime Achievement and the APS Heineman Prize in Mathematical Physics.

'This remarkable near-encyclopaedic volume will become a classic text. Barry Simon's vision and knowledge are evident on every page, and the result is a must-have for experts and students alike. The material proceeds from the classical to the ultra-modern, including recent probabilistic methodology and a fascinating list of open problems.' Geoffrey Grimmett, University of Cambridge

• Notation; 1. A framework for lattice gases; 2. Correlation inequalities; 3. The Lee-Yang theorem; 4. Peierls argument; 5. No continuous symmetry breaking in 2D (and other situations); 6. Infrared bounds; 7. Stochastic geometric representations; 8. Berezinskii-Kosterlitz-Thouless transition; 9. Final thoughts; References; Author index; Subject index.

Barry Simon is a mathematical physicist who has served on the faculty of Princeton and Caltech. Noted for his many books and research contributions, his honours include the AMS Steele Prize for Lifetime Achievement and the APS Heineman Prize in Mathematical Physics.

'This remarkable near-encyclopaedic volume will become a classic text. Barry Simon's vision and knowledge are evident on every page, and the result is a must-have for experts and students alike. The material proceeds from the classical to the ultra-modern, including recent probabilistic methodology and a fascinating list of open problems.' Geoffrey Grimmett, University of Cambridge

• Notation; 1. A framework for lattice gases; 2. Correlation inequalities; 3. The Lee-Yang theorem; 4. Peierls argument; 5. No continuous symmetry breaking in 2D (and other situations); 6. Infrared bounds; 7. Stochastic geometric representations; 8. Berezinskii-Kosterlitz-Thouless transition; 9. Final thoughts; References; Author index; Subject index.