Spontaneous Symmetry Breaking and the Transition to Disorder in Physics

A brief review of disorder systems in Statistical Physics is presented using the framework of the Ising model. Associated properties are described in terms of a social metaphor with a collection of people wearing either red or green shirts. Firstly, the ferromagnetic case is studied in detail to present both mechanisms of spontaneous symmetry-breaking and continuous order-disorder transition. The concept of phase diagram is explained as well as the role of thermal fluctuations in the universal properties associated with a critical phenomenon.The effect of an external uniform field is also presented together with the notion of first order phase transition. Then various disorder systems are reviewed, such as having competing exchange interactions leading to spin glasses, and random local fields leading to the random field model.