PHZ3400 Symmetry Breaking

Classification of Phases: Symmetry

insert ==> critical phenomena

==>definition of symmetry A general definition of symmetry can be described as a precise and well defined concept of balance between two objects or functions. Symmetry can be found in many things in physics from the standard model, spacetime and supersymmetry. To our study in condensed matter, symmetry can be seen in crystals, magnets, superconductors, superfluids and their behaviors among multiple outside forces. ==>symmetry in phase transitions

==>symmetry breaking Symmetry Breaking can be described as the potential to for a symmetry of some system to fall from its symmetric properties and move into one direction or the other.

Spontaneous Symmetry Breaking and Thermodynamic Limit

Spontaneous Symmetry Breaking or SSB is refering to when an outside force interacts with the system, it will induce the falling out of symmetry very easily and sometimes rapidly.

Ferromagnet and Curie-Weiss Theory

The ferromagnet is defined as any material which can exhibit magnetic properties or be induced by an external magnetic field. This property identifies it as a possible permanent magnet. These properties are determined by all the atoms within the material to align in some general direction depending on the structure of the material. The alignments are determined by the dipole moment found in the atom due to the electrons spin and angular momentum. Each dipole being induced by the neighboring dipoles will by classical theory cause the dipoles to alternate direction. However this force is greatly outweighed by the effect of the Pauli principle and the dipoles will align in the same direction. This property should keep the magnetic field in one direction, but is not seen among most ferromagnetic materials. Once a large system is considered with thousands of ions, classical forces will now outweigh quantum properties of the Pauli principle. This will create what are called magnetic domains in which large sections of ions are aligned in one direction and then there is an opposing section of oppositely aligned ions. Between these two sections is what is called the domain wall where the dipoles will be opposing on each side of the wall. This gives the effect of a neutral material with no magnetic field since they cancel each other out.

So why when a magnetic field is induced into a material and then removed, does it not fall back to its original state? This situation causes all or most of the dipoles to flip and become locked into the same direction. Among the lattice of the material, when each ion flips it forces its way past defects in the lattice, causing it to become locked into position when the field is removed.

The relationship between magnetic susceptibility versus temperature is linked through the Curie temperature of the material. Combining equations of Curie's Law and magnetic susceptibility, the Curie-Weiss law is formed.

$\chi ={\frac {C}{T-T_{c}}}$

The denominator can become undefined, which is alarming. In nature, this represents spontaneous magnetization when T = T_c or below.

Caution must be taken near the critical point, in this case Curie Point. The mean field approximation does not accurately represent critical behavior nearby the critical point.

Other Examples of Symmetry Breaking

Other Examples of Symmetry Breaking Include:

Explicit symmetry breaking happens when the actual laws of the system are not invariant for the symmetry in question.

Dynamical symmetry breaking is a special form of spontaneous symmetry breaking. (Fermion condensates)

Chiral Symmetry Breaking