Ising model

Isingov model je matematički model uveden kao pojednostavljeni prikaz feromagnetizma u statističkoj fizici i kao takav bavi se fizikom faznih prijelaza. Model sadrži varijable diskretnih vrijednosti ±1, koje predstavljaju magnetske dipolne momente atoma – spinove. Osnovna pretpostavka modela je interakcija spina samo s njegovim najbližim susjedima. U jednodimenzionalnom Isingovom modelu pokazuje se nepostojanje faznoga prijelaza, osim pri temperaturi apsolutne nule. Landauova teorija faznih prijelaza dovodi do zaključka da se u dvodimenzionalnom Isingovom modelu javlja fazni prijelaz drugoga reda pri prelasku sistema iz feromagnetske u paramagnetsku fazu. Monte Carlo simulacijom generira se kvadratna rešetka dvodimenzionalnog Isingovog modela te se računaju termodinamičke veličine prosječne energije, magnetizacije i toplinskog kapaciteta, čija interpretacija dovodi do zaključka o pojavi i vrsti faznoga prijelaza. The Ising model is a mathematical model introduced as a simplified representation of ferromagnetism in statistical physics and, as such, is concerned with the physics of phase transitions. The model consists of variables with discrete values ±1 that represent magnetic dipole moments of atoms - spins. The model assumes that each spin has only nearestneighbour interaction. Phase transition in the one-dimensional Ising model does not occur except at absolute zero temperature. Landau’s theory of phase transitions leads to the conclusion that in the two-dimensional Ising model, a phase transition of the second order occurs during the system’s transition from the ferromagnetic to the paramagnetic phase. Monte Carlo simulation generates a square lattice of the two-dimensional Ising model and calculates the thermodynamic quantities of average energy, magnetization and heat capacity, the interpretation of which leads to a conclusion about the occurrence and type of phase transition.