The concept of spontaneous symmetry breaking is closely related to phase transitions in condensed matter physics. Phase transitions occur when a substance undergoes a change in its physical properties, such as its symmetry, structure, or behavior, as a result of external conditions such as temperature, pressure, or magnetic field.
Spontaneous symmetry breaking is a phenomenon that can occur during a phase transition. It happens when a system that possesses a particular symmetry at the microscopic level exhibits a lower symmetry at the macroscopic or observable level. In other words, even though the underlying laws of physics are symmetric, the system as a whole appears to have a broken symmetry.
In condensed matter physics, phase transitions are often associated with changes in the arrangement or alignment of atoms or molecules within a material. For example, consider the case of a ferromagnet, a material that exhibits spontaneous magnetization below a certain critical temperature, called the Curie temperature. Above the Curie temperature, the material's magnetic moments (spins) are randomly oriented, resulting in no net magnetization and a high-temperature phase. However, as the temperature decreases below the Curie temperature, the magnetic moments align spontaneously, leading to a low-temperature phase with a non-zero magnetization. This alignment breaks the rotational symmetry of the material.
Another example is the phase transition between the liquid and solid states of matter. In the liquid phase, the particles are free to move and do not exhibit long-range order. However, as the temperature decreases, the particles start to arrange themselves in a regular, periodic lattice structure, forming a solid. This transition breaks the translational symmetry of the system.
Spontaneous symmetry breaking in condensed matter systems can give rise to the emergence of new collective phenomena and excitations, such as phonons, magnons, or Cooper pairs in superconductors. These broken symmetry states are often associated with the formation of order parameters, which are macroscopic quantities that indicate the broken symmetry in the system.
Overall, the concept of spontaneous symmetry breaking provides a framework to understand and describe the changes in symmetry and properties that occur during phase transitions in condensed matter physics. It helps us understand how collective behavior arises from the interactions of individual constituents and how new macroscopic phenomena can emerge from the underlying microscopic laws.