# Complex Saddle Points and Disorder Lines in QCD at finite temperature and density

Nishimura H, Ogilvie MC, Pangeni K (2015) *Physical Review D* 91: 054004.

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The properties and consequences of complex saddle points are explored inphenomenological models of QCD at non-zero temperature and density. Such saddlepoints are a consequence of the sign problem, and should be considered in boththeoretical calculations and lattice simulations. Although saddle points infinite-density QCD are typically in the complex plane, they are constrained bya symmetry that simplifies analysis. We model the effective potential forPolyakov loops using two different potential terms for confinement effects, andconsider three different cases for quarks: very heavy quarks, massless quarkswithout modeling of chiral symmetry breaking effects, and light quarks withboth deconfinement and chiral symmetry restoration effects included in a pairof PNJL models. In all cases, we find that a single dominant complex saddlepoint is required for a consistent description of the model. This saddle pointis generally not far from the real axis; the most easily noticed effect is adifference between the Polyakov loop expectation values $\left\langle {\rmTr}_{F}P\right\rangle $ and $\left\langle {\rm Tr}_{F}P^{\dagger}\right\rangle$, and that is confined to small region in the $\mu-T$ plane. In all but onecase, a disorder line is found in the region of critical and/or crossoverbehavior. The disorder line marks the boundary between exponential decay andsinusoidally modulated exponential decay of correlation functions. Disorderline effects are potentially observable in both simulation and experiment.Precision simulations of QCD in the $\mu-T$ plane have the potential to clearlydiscriminate between different models of confinement.

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Nishimura H, Ogilvie MC, Pangeni K. Complex Saddle Points and Disorder Lines in QCD at finite temperature and density.

*Physical Review D*. 2015;91:054004.Nishimura, H., Ogilvie, M. C., & Pangeni, K. (2015). Complex Saddle Points and Disorder Lines in QCD at finite temperature and density.

*Physical Review D*,*91*, 054004. doi:10.1103/physrevd.91.054004Nishimura, H., Ogilvie, M. C., and Pangeni, K. (2015). Complex Saddle Points and Disorder Lines in QCD at finite temperature and density.

*Physical Review D*91, 054004.Nishimura, H., Ogilvie, M.C., & Pangeni, K., 2015. Complex Saddle Points and Disorder Lines in QCD at finite temperature and density.

*Physical Review D*, 91, p 054004. H. Nishimura, M.C. Ogilvie, and K. Pangeni, “Complex Saddle Points and Disorder Lines in QCD at finite temperature and density”,

*Physical Review D*, vol. 91, 2015, pp. 054004. Nishimura, H., Ogilvie, M.C., Pangeni, K.: Complex Saddle Points and Disorder Lines in QCD at finite temperature and density. Physical Review D. 91, 054004 (2015).

Nishimura, Hiromichi, Ogilvie, Michael C., and Pangeni, Kamal. “Complex Saddle Points and Disorder Lines in QCD at finite temperature and density”.

*Physical Review D*91 (2015): 054004.
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