TY - JOUR

T1 - Zeroing in on SU(3)

AU - Karliner, Marek

AU - Sharpe, Stephen R.

AU - Chang, Y. F.

N1 - Funding Information:
It is an old idea that one should study the thermodynamic properties of a system by following the movement of the zeroes of its partition function \[1-5\].T he zeroes of the partition function in the complex temperature plane determine the behaviour of thermodynamic quantities at real temperatures, much as the poles of the S-matrix in the complex energy plane determine scattering amplitudes at real energies. Recently, the application of this approach to lattice gauge theories has been given new impetus by the suggestion of a practical method to calculate the density of states for large systems. \[6,7 \]*. Given the density of states, one can reconstruct the partition function and find its zeroes. We find this approach, which we refer to as * Work supported by the Department of Energy, contract DE-AC03-76SF00515. * Other methods for calculating the density of states have been presented in the statistical mechanics literature, and applied to small systems. For a comprehensive discussion see the review of Binder \[8\]. Partition functions have also been constructed for random surface models \[9\].

PY - 1988/5/30

Y1 - 1988/5/30

N2 - We present an improved numerical method for calculating the density of states for lattice field theories. We use it to study the SU(3) pure gauge theory at both zero and finite temperature. We also compute strong and weak coupling expansions for the density of states and find excellent agreement with our data. Using a specially developed algorithm for solving high-order polynomials, we find the zeroes of the partition function. For lattices with Lt = 2, we test the finite-size scaling prediction for the rounding of the transition by following the motion of these zeroes for Ls=6, 8, 10, and 12. We find that the correlation length exponent is 1/v = 3.02 ± 0.05, in excellent agreement with the value d=3 expected for a first-order deconfinement transition.

AB - We present an improved numerical method for calculating the density of states for lattice field theories. We use it to study the SU(3) pure gauge theory at both zero and finite temperature. We also compute strong and weak coupling expansions for the density of states and find excellent agreement with our data. Using a specially developed algorithm for solving high-order polynomials, we find the zeroes of the partition function. For lattices with Lt = 2, we test the finite-size scaling prediction for the rounding of the transition by following the motion of these zeroes for Ls=6, 8, 10, and 12. We find that the correlation length exponent is 1/v = 3.02 ± 0.05, in excellent agreement with the value d=3 expected for a first-order deconfinement transition.

UR - http://www.scopus.com/inward/record.url?scp=0001132857&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(88)90242-8

DO - 10.1016/0550-3213(88)90242-8

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AN - SCOPUS:0001132857

VL - 302

SP - 204

EP - 250

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2

ER -