Physics of phase transitions

Objectives of the course are to provide the student with the contemporary state of the art in the field of statistical physics and to introduce him to the statistical physics ideas, models, approaches and methods. Students will understand methods, ideas and approaches to phase transitions and critical phenomena.

Mat. Analysis I, II Linear Algebra Statistical Mechanics

I. NON-IDEAL GASES
Deviation of gases from the ideal state; Expansion in powers of the density; Van der Waals' formula. 5hrs
II. PHASE EQUILIBRIUM AND PHASE TRANSITIONS OF Ist ORDER
Conditions of phase equilibrium; The Clapeyron-Clausius formula; The critical point; The law of corresponding states;
Definition of
phase transition and its classification by Ehrenfest.
III. SOLUTIONS
Systems, containing different particles; The phase rule; Weak solutions; Osmotic pressure; Solvent phases in contact; Mixture of ideal gases; Vapor pressure over concentrated solution.
IV. THE ISING MODEL
Definition of the Ising model; Equivalence to other models; Spontaneous magnetization; The Bragg-Williams approximation; The Bethe- Pierls approximation; 1D Ising model and Landau-Pierls theorem.
V. CRITICAL PHENOMENA
The order parameter; The correlation function and the Fluctuation-Dissipation theorem; Critical exponents; The scaling hypothesis; Scale invariance; Goldstone excitations; The importance of dimensionality.
VI. THE LANDAU APPROACH
Landau free energy; Mathematical digression; Derivation in simple models; Mean-field theory; The Van der Waals equation of state; Tricritical point; Gaussian model; Ginzburg criterion; Anomalous dimensions.

Students will gain understanding of what phase transitions are and the relevant terminology and concepts used in the field.

• K. Huang, Statistical mechanics. New York: Wiley (1987). Catalogue E-version
• L. D. Landau, E. M. Lifshitz: 'Statistical Physics (Third Edition, Part 1: Volume 5 (Course of Theoretical Physics, Volume 5, first printed 1980, reprinted 1982,1985, 1986, 1988, 1993, 1994, 1996, 2000, 2001, 2003, 2005). Catalogue

• written tests, writen exam
• oral exam

Dr. Artem Badasyan je izredni profesor za področje fizike na Univerzi v Novi Gorici. Dr. Artem Badasyan is associate professor of Physics at University of Nova Gorica.
1. MACHREKI, Manel, BADASYAN, Artem, ŽIGON, Dušan, TYULIEV, Georgi, EMIN, Saim.
Photoelectrochemical conversion of biomass alcohols using in-situ Sn-doped α−Fe2O3 thin films. Journal of environmental chemical engineering. [Online ed.]. Feb. 2025, vol. 13, issue 1, [article no.] 115363, str. 1-9, ilustr. ISSN 2213-3437.
https://www.sciencedirect.com/science/article/pii/S2213343725000582, Repozitorij Univerze v Novi Gorici - RUNG, DOI: 10.1016/j.jece.2025.115363. [COBISS.SI-ID 221378563]
2. STEPANYAN, V., BADASYAN, Artem, MOROZOV, V., MAMASAKHLISOV, Yevgeni S.,
PODGORNIK, Rudolf. Sequence disorder-induced first order phase transition in confined polyelectrolytes. The Journal of chemical physics. 2024, vol. 161, issue 13, [article no.] 134906, str. 1-11, ilustr. ISSN 0021-9606. Repozitorij Univerze v Novi Gorici - RUNG, DOI: 10.1063/5.0228162. [COBISS.SI-ID 210190595]
3. ASATRYAN, Arevik V., BENIGHT, Albert S., BADASYAN, Artem. Origins of fine structure in DNA melting curves. The Journal of chemical physics. 7. Aug. 2024, vol. 161, issue 5, [article no.] 055103, str. 1-8, ilustr. ISSN 0021-9606.
https://pubs.aip.org/aip/jcp/article/161/5/055103/3306959/Origins-of-fine-structure-in-DNA- melting-curves, Repozitorij Univerze v Novi Gorici - RUNG, DOI: 10.1063/5.0213526. [COBISS.SI-ID 203943939]
4. YERITSYAN, Knarik, BADASYAN, Artem. Differential scanning calorimetry of proteins and Zimm- Bragg model in water. Archives of biochemistry and biophysics. Oct. 2024, vol. 760, [article no.] 110132, str. 1-6, ilustr. ISSN 0003-9861. https://www.sciencedirect.com/science/article/pii/S0003986124002546, Repozitorij Univerze v Novi Gorici - RUNG, DOI: 10.1016/j.abb.2024.110132. [COBISS.SI-ID 205311491]
5. YERITSYAN, Knarik, BADASYAN, Artem. Differential scanning calorimetry of proteins and the two- state model : comparison of two formulas. Biophysica. Jun. 2024, vol. 4, issue 2, str. 227-237, ilustr. ISSN 2673-4125. https://www.mdpi.com/2673-4125/4/2/16, Repozitorij Univerze v Novi Gorici - RUNG, DOI: 10.3390/biophysica4020016. [COBISS.SI-ID 196140291]