Optimierte Borelsummation von kritischen Exponenten und universellen Amplitudenverhältnissen im phi 4-Modell

Second order phase transitions are investigated with theoretical methods of the phi^4 field theory. Thermodynamic quantities like the correlation length, the susceptibility or the specific heat have singularities in the critical point. The goal is the precise temperature dependence near these singularities. A cooperative many particel effect generates critical behavior. Differences in the short range microscopic interaction of the investigated systems are insignificant. The dimension d and the number of components of the order parameter determine the critical behavior. The renormalization group theory identifies universality classes of critical behavior and predicts that critical exponents and certain amplitude ratios are equal for all systems of the same universality class. The case d=3, n=2 is of special interest. Experimental results of the superfluid transition of 4^He in space are compared to MC simulations of spin systems and analytical calculations in the framework of the phi^4 theory. This is a high precision test of the RG prediction of universality. RG theory has a wide range of applications. Hence, this quantitative test of RG is of interest in statistical physics, condensed matter physics and elementary particle physics. A short summary of two main results: A significant improvement of former Borel summations of critical exponents gamma and alpha is achieved with the same information of perturbation series. This improvement stems from an enhancement of the method of resummation. Amplitude functions at the fixpoint are resummed. Analytical results for certain universal amplitude ratios are achieved. So far only numerical or experimental quantitative results for these ratios are known.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2008

Author dc:creator

• Cremer, Daniel

Contributors dc:contributor

• Dohm, Volker

• info:eu-repo/classification/ddc/530
• Physik
• Phasenübergänge
• kritische Exponenten
• universelle Amplitudenverhältnisse
• phase transitions
• critical exponents
• universal amplitude ratios

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-112576%22

OAI record oai:identifier

https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A50011