Ising model
| Autor: | Pavlina, Anamarija |
|---|---|
| Přispěvatelé: | Horvatić, Davor |
| Jazyk: | chorvatština |
| Rok vydání: | 2022 |
| Předmět: |
Isingov model
Landauova teorija transition temperature prijelazna temperatura magnetization NATURAL SCIENCES. Physics magnetizacija phase transitions PRIRODNE ZNANOSTI. Fizika PRIRODNE ZNANOSTI. Matematika Ising model fazni prijelazi NATURAL SCIENCES. Mathematics Monte Carlo simulacija Landau theory Monte Carlo simulation |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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