TY - JOUR

T1 - Monte Carlo calculations with dynamical fermions by a local stochastic process

AU - Rossi, Pietro

AU - Zwanziger, Daniel

N1 - Funding Information:
Monte Carlo calculations with quarks were originally done in the quenched or valence approximation which neglects the influence of the quarks on the gluon distribution \[1-3\].M ethods \[4-1 1\] which do account for the fermionic determinant either contain a systematic error of unknown size \[12\]o r, if exact, suffer from various drawbacks such as requiring an amount of computer time which grows faster than Dean's Dissertation Fellow. 2 This research was supported in part by the National Science Foundation under grant no. PHY-8116102. 261

PY - 1984/9/3

Y1 - 1984/9/3

N2 - We develop and test numerically a Monte Carlo method for fermions on a lattice which accounts for the effect of the fermionic determinant to arbitrary accuracy. It is tested numerically in a 4-dimensional model with SU(2) color group and scalar fermionic quarks interacting with gluons. Computer time grows linearly with the volume of the lattice and the updating of gluons is not restricted to small jumps. The method is based on random location updating, instead of an ordered sweep, in which quarks are updated, on the average, R times more frequently than gluons. It is proven that the error in R is only of order 1/R instead of 1/R 1 2 as one might naively expect. Quarks are represented by pseudofermionic variables in M pseudoflavors (which requires M times more memory for each physical fermionic degree of freedom) with an error in M of order 1/M. The method is tested by calculating the self-energy of an external quark, a quantity which would be infinite in the absence of dynamical or sea quarks. For the quantities measured, the dependence on R-1 is linear for R ≥ 8, and, within our statistical uncertainty, M = 2 is already asymptotic.

AB - We develop and test numerically a Monte Carlo method for fermions on a lattice which accounts for the effect of the fermionic determinant to arbitrary accuracy. It is tested numerically in a 4-dimensional model with SU(2) color group and scalar fermionic quarks interacting with gluons. Computer time grows linearly with the volume of the lattice and the updating of gluons is not restricted to small jumps. The method is based on random location updating, instead of an ordered sweep, in which quarks are updated, on the average, R times more frequently than gluons. It is proven that the error in R is only of order 1/R instead of 1/R 1 2 as one might naively expect. Quarks are represented by pseudofermionic variables in M pseudoflavors (which requires M times more memory for each physical fermionic degree of freedom) with an error in M of order 1/M. The method is tested by calculating the self-energy of an external quark, a quantity which would be infinite in the absence of dynamical or sea quarks. For the quantities measured, the dependence on R-1 is linear for R ≥ 8, and, within our statistical uncertainty, M = 2 is already asymptotic.

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U2 - 10.1016/0550-3213(84)90028-2

DO - 10.1016/0550-3213(84)90028-2

M3 - Article

AN - SCOPUS:48549111596

SN - 0550-3213

VL - 243

SP - 261

EP - 272

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 2

ER -