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Determination of the order of phase transition in the one-dimensional Potts model with long-range interactions


Glumac, Zvonko; Uzelac, Katarina
Determination of the order of phase transition in the one-dimensional Potts model with long-range interactions // Conference of the Middle European Cooperation in Statistical Physics - MECO 29
Bratislava, 2004. (poster, međunarodna recenzija, sažetak, znanstveni)


Naslov
Determination of the order of phase transition in the one-dimensional Potts model with long-range interactions

Autori
Glumac, Zvonko ; Uzelac, Katarina

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Conference of the Middle European Cooperation in Statistical Physics - MECO 29 / - Bratislava, 2004

Skup
Conference of the Middle European Cooperation in Statistical Physics - MECO '29

Mjesto i datum
Bratislava, 28 MARCH - 1 APRIL 2004

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Long-range interactions; Potts model; scaling

Sažetak
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 $q$.

Izvorni jezik
Engleski

Znanstvena područja
Fizika



POVEZANOST RADA


Projekt / tema
0035007