Determination of the order of phase transition in the one-dimensional Potts model with long-range interactions (CROSBI ID 503848)
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Podaci o odgovornosti
Glumac, Zvonko ; Uzelac, Katarina
engleski
Determination of the order of phase transition in the one-dimensional Potts model with long-range interactions
We discuss the determination of the order of transition in the one-dimensional ferromagnetic $q$-state Potts model with long-range (power-law and mean-field) interactions, within three different approaches. The first approach is by finite-range scaling, a kind of phenomenological renormalisation group where the finite range $L$ has been used as a basic scaling quantity. The spectrum of transfer matrix iz analyzed in different regimes. We further discuss the approach by Monte Carlo simulations, where the order of transition is determined from the scaling behaviour of the quantities derived from the moments of the energy probability distibution. Last we present the results obtained by studying the partition function zeroes in the complex plane of an appropriate parameter. After presenting the partition function in the form of the polynomial in $q$, the number of states, we analyzed its zeros in the complex-$q$ plane. The order of trasinion was determined from the scaling of the zero closest to the real axis. All three approaches are applicabile on models with both integer and continous values of number of Potts states $q$.
long-range interactions; Potts model; scaling
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Podaci o prilogu
2004.
objavljeno
Podaci o matičnoj publikaciji
Conference of the Middle European Cooperation in Statistical Physics - MECO 29
Bratislava:
Podaci o skupu
Conference of the Middle European Cooperation in Statistical Physics - MECO '29
poster
28.03.2004-01.04.2004
Bratislava, Slovačka