5
Despite making use of a diﬀerent approach, in general
we ﬁnd good qualitative agreement with the res ults re-
ported in Refs. [
18, 19] after dropping S
g
, i.e. for β = 0.
IV. Conclusions
In this paper we have constructed one-dimensional lat-
tice models re sembling QED and QCD to investigate the
ﬁnite density and ﬁnite temperature regime. Despite the
drastic simpliﬁcations in these models, they capture some
essential physical properties e xpected from the full theory
and show an interesting behavior of the Polyakov loop.
We found that they—like their four-dimensional contin-
uous counterparts—exhibit the Silver Blaze property in
the zero temperature limit N → ∞. The µ-dependence
of the SU(3) (conjuga te) Polyakov loop P (P
†
) show s
the pec uliar µ-dependence also found in other approx-
imations of QCD. The models presented her e ca n also
serve as a starting point for the construction of mo re
elaborated models.
V. Acknowledgments
This work is supported by the Helmholtz Alliance
HA216/EMMI and by ERC-AdG-290623. J.M.P. thanks
the Yukawa Institute for Theoretical Physics, Kyoto Uni-
versity, where this work was completed during the YITP-
T-13-0 5 on ’New Frontiers in QCD’. I.-O.S. thanks the
Deutsche Forschungsgemeinschaft by STA 283/1 6-1 and
C.Z. thanks Nanya ng Technological University for sup-
port.
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