phase transition

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1、PhaseTransitionsProseminarinTheoreticalPhysicsInstitutfurtheoretischePhysik¨ETHZurich¨SS07typeset&compilationbyH.G.Katzgraber(withhelpfromF.Hassler)TableofContents1Symmetryandergodicitybreaking,mean-fieldstudyoftheIsingmodel11.1Introduction..................

2、............11.2Formalism...............................21.3Themodelsystem:Isingmodel...................41.4Solutionsinoneandmoredimensions................81.5Symmetryandergodicitybreaking.................141.6Concludingremarks..........................172Cr

3、iticalPhenomenainFluids212.1RepetitionoftheneededThermodynamics.............212.2Two-phaseCoexistence........................232.3VanderWaalsequation.......................262.4Spatialcorrelations..........................302.5Determinationofthecriticalpoint

4、/difficultiesinmeasurement..323LandauTheory,FluctuationsandBreakdownofLandauThe-ory373.1Introduction..............................373.2LandauTheory............................403.3Fluctuations..............................443.4ConclusiveWords..................

5、.........494Scalingtheory534.1Criticalexponents...........................534.2Scalinghypothesis..........................544.3DerivingtheHomogeneousforms..................584.4Universalityclasses..........................614.5Polymerstatistics..............

6、.............624.6Conclusions..............................68iiiTABLEOFCONTENTS5TheRenormalizationGroup715.1Introduction..............................715.2Classicallatticespinsystems.....................725.3Scalinglimit..............................735.4Ren

7、ormalizationgrouptransformations...............765.5Example:TheGaussianfixedpoint.................836CriticalslowingdownandclusterupdatesinMonteCarlosimulations896.1Introduction..............................896.2Criticalslowingdown.........................926

8、.3Clusterupdates............................956.4Concludingremarks..........................1017Finite-SizeScaling1057.1Introduction..............................1057.2ScalingFunctionHypothesis.