TY - JOUR
T1 - Why Might the Standard Large N Analysis Fail in the O (N) Model
T2 - The Role of Cusps in Fixed Point Potentials
AU - Yabunaka, Shunsuke
AU - Delamotte, Bertrand
N1 - Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/12/4
Y1 - 2018/12/4
N2 - The large N expansion plays a fundamental role in quantum and statistical field theory. We show on the example of the O(N) model that at N= its standard implementation misses some fixed points of the renormalization group in all dimensions smaller than four. These new fixed points show singularities under the form of cusps at N= in their effective potential that become a boundary layer at finite N. We show that they have a physical impact on the multicritical physics of the O(N) model at finite N. We also show that the mechanism at play holds also for the O(N) - O(2) model and is thus probably generic.
AB - The large N expansion plays a fundamental role in quantum and statistical field theory. We show on the example of the O(N) model that at N= its standard implementation misses some fixed points of the renormalization group in all dimensions smaller than four. These new fixed points show singularities under the form of cusps at N= in their effective potential that become a boundary layer at finite N. We show that they have a physical impact on the multicritical physics of the O(N) model at finite N. We also show that the mechanism at play holds also for the O(N) - O(2) model and is thus probably generic.
UR - http://www.scopus.com/inward/record.url?scp=85057730795&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85057730795&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.121.231601
DO - 10.1103/PhysRevLett.121.231601
M3 - Article
C2 - 30576204
AN - SCOPUS:85057730795
VL - 121
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 23
M1 - 231601
ER -