Developments in the theory of universality

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Developments in the theory of universality Vieri Mastropietro Rome University ”Tor Vergata”

  • tor vergata

  • vieri mastropietro

  • precise test

  • shuttle experiments

  • physics says

  • universality allow testable


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Developments in the theory universality
Vieri Mastropietro
Rome University Tor Vergata”
of
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The universality hypothesis (well confirmed by experiments) in statistical physics says that a number of macroscopic critical properties are largely independent of the microscopic structure, at least inside a universality class of systems.
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Universality in stastistical physics
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Universality in stastistical physics
The universality hypothesis (well confirmed by experiments) in statistical physics says that a number of macroscopic critical properties are largely independent of the microscopic structure, at least inside a universality class of systems. Precise test for universality in shuttle experiments for helium (2000); agreement with several digits.
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noCtcenlacidleoeht.)yr
The universality hypothesis (well confirmed by experiments) in statistical physics says that a number of macroscopic critical properties are largely independent of the microscopic structure, at least inside a universality class of systems. Precise test for universality in shuttle experiments for helium (2000); agreement with several digits. Universality allow testable predictions even if we do not known the details of the microscopic model.
Universality in stastistical physics
FQaTdntstasiitaclphysics(statistoitazilaocpeeD.nontiecnnenteewsbebwtoisnineveeunityarsalnormndre
Universality in stastistical physics
The universality hypothesis (well confirmed by experiments) in statistical physics says that a number of macroscopic critical properties are largely independent of the microscopic structure, at least inside a universality class of systems. Precise test for universality in shuttle experiments for helium (2000); agreement with several digits. Universality allow testable predictions even if we do not known the details of the microscopic model. Connections between universality and renormalization. Deep connections bewteen QFT and statistical physics (statistical field theory).
The Ising model
The paradigmatic model for statistical mechanics is the 2D Ising model
H=JX Xσxσx+ejXhx j=0,1xΛxΛ
σx=±, Λ is a square lattice,xΛ,e0= (0,1),e1= (1,0).
phase
Thepartition functionisZ=PσeβH(σ)and transitions appear as non-analyticity points of 1 fβ=βlim|Λ||Λ1|logZ.
orJm.
Ising model
The
pendentfi.e.indeβ>edxhyhβ=<cro6βananerthfastcays>yhxh<2C+|cββ|gefilwh|2y|xCβccilaniidT.ehrctirenumbercesarepu|1ξ|yxwopyfore|TCc|Tit,w1hξcaltritiratuempeathnersi21cβ=JOn(91(regascehT))44ve)andthecorrelaitnoCs(v)β1Coldtanspheieceaches(tdnocireditav
The Ising model
Thepartition functionisZ=PσeβH(σ)and phase transitions appear as non-analyticity points of fβ=β1lim|Λ||Λ1|logZ. (Onsager (1944)) The critical temperature is tanhβcJ=21 and the specific heat (second derivative) and the correlations
Cv(β)∼ −C1log|ββc|+C2<hxhy>βc|xCy|2
while forβ6=βc<hxhy>βdecays faster than any power ofξ1|xy|, withξ1C|TTc|. Thecritical indices arepure numberi.e. independent fromJ.