scholarly journals A Lattice Test of Alternative Interpretations of "Triviality" in (λΦ4)4 Theory

1997 ◽  
Vol 12 (14) ◽  
pp. 1011-1024 ◽  
Author(s):  
A. Agodi ◽  
G. Andronico ◽  
P. Cea ◽  
M. Consoli ◽  
L. Cosmai ◽  
...  
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Higgs Mass ◽  
Higgs Field ◽  
Alternative Interpretation ◽  
Lattice Data ◽  
First Order ◽  
Conventional Picture ◽  
The Continuum ◽  
Second Order Phase Transition

There are two physically different interpretations of "triviality" in (λΦ4)4 theories. The conventional description predicts a second-order phase transition and that the Higgs mass mh must vanish in the continuum limit if v, the physical vev is held fixed. An alternative interpretation, based on the effective potential obtained in "triviality-compatible" approximations (in which the shifted "Higgs" field h(x)≡Φ(x)-<Φ> is governed by an effective quadratic Hamiltonian) predicts a phase transition that is very weakly first-order and that mh and v are both finite, cutoff-independent quantities. To test these two alternatives, we have numerically computed the effective potential on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. All give excellent agreement with the literature value. Two different methods for obtaining the effective potential were used, as a control on the results. Our lattice data are fitted very well by the predictions of the unconventional picture, but poorly by the conventional picture.

scholarly journals DEVELOPMENT OF THE ELECTROWEAK PHASE TRANSITION AND BARYOGENESIS

2000 ◽  
Vol 09 (06) ◽  
pp. 733-755 ◽  
Author(s):  
ARIEL MÉGEVAND
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Effective Potential ◽  
Significant Variation ◽  
Higgs Field ◽  
Small Interval ◽  
Electroweak Phase Transition ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

We investigate the evolution of the electroweak phase transition, using a one-Higgs effective potential that can be regarded as an approximation for the Minimal Supersymmetric Standard Model. The phase transition occurs in a small interval around a temperature Tt below the critical one. We calculate this temperature as a function of the parameters of the potential and of a damping coefficient related to the viscosity of the plasma. The parameters that are relevant for baryogenesis, such as the velocity and thickness of the walls of bubbles and the value of the Higgs field inside them, change significantly in the range of temperatures where the first-order phase transition can occur. However, we find that in the likely interval for Tt there is no significant variation of these parameters. Furthermore, the temperature Tt is in general not far below the temperature at which bubbles begin to nucleate.

Ring-diagram summations in the finite-temperature effective potential

1993 ◽  
Vol 71 (5-6) ◽  
pp. 227-236 ◽  
Author(s):  
M. E. Carrington
Keyword(s):  
Phase Transition ◽  
Standard Model ◽  
Effective Potential ◽  
Finite Temperature ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Ring Diagram ◽  
First Order Phase Transition ◽  
The Standard Model ◽  
The One

There has been much recent interest in the finite-temperature effective potential of the standard model in the context of the electroweak phase transition. We review the calculation of the effective potential with particular emphasis on the validity of the expansions that are used. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electroweak phase transition. However, in the high-temperature regime, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram summation, and show that the standard model has a first-order phase transition in the weak coupling expansion.

PHASE TRANSITION IN $g\varphi^4_2$ THEORY

1992 ◽  
Vol 07 (24) ◽  
pp. 2189-2197 ◽  
Author(s):  
G. V. EFIMOV ◽  
G. GANBOLD
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Effective Potential ◽  
Variational Approach ◽  
Two Dimensions ◽  
Second Order ◽  
Complete Agreement ◽  
Vacuum Stability ◽  
Second Order Phase Transition

The vacuum stability of a scalar gφ4 theory in two dimensions is studied. A variational approach is applied to estimate the effective potential in this model. We find that the second order phase transition takes place. It is in complete agreement with the Simon-Griffiths theorem.

CRITICAL BEHAVIOR OF THE SPECIFIC HEAT IN THE VICINITY OF THE TRANSITION TEMPERATURE FOR S-TRIAZINE

2009 ◽  
Vol 23 (09) ◽  
pp. 2253-2259 ◽  
Author(s):  
M. KURT ◽  
H. YURTSEVEN
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Transition Temperature ◽  
Critical Exponent ◽  
Specific Heat ◽  
Power Law ◽  
Order Phase Transition ◽  
Critical Behavior ◽  
First Order ◽  
Second Order Phase Transition

The critical behavior of the specific heat is studied in s-triazine ( C 3 N 3 H 3). Using the experimental data for the CP, the temperature dependence of the specific heat is analyzed according to a power-law formula and the values of the critical exponent for CP are extracted in the vicinity of the transition temperature (TC=198.07 K ). It is indicated that s-triazine undergoes a weakly first order (quasi-continuous) or second order phase transition.

THE ELECTROWEAK PHASE TRANSITION ON THE LATTICE

1994 ◽  
Vol 05 (02) ◽  
pp. 379-381
Author(s):  
K. FARAKOS ◽  
K. KAJANTIE ◽  
K. RUMMUKAINEN ◽  
M. SHAPOSHNIKOV
Keyword(s):  
Phase Transition ◽  
Higgs Mass ◽  
Big Bang ◽  
Higgs Particle ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Lattice Monte Carlo ◽  
The Big Bang ◽  
The Universe ◽  
Detailed Nature

According to the electroweak baryogenesis scenario the matter-antimatter asymmetry of the Universe was created shortly after the Big Bang, during the electroweak phase transition. This process depends strongly on the detailed nature of the electroweak phase transition. For realistic Higgs particle masses, the standard perturbative analysis indicates that the transition is at most only weakly first order. We have studied the transition with non-perturbative lattice Monte Carlo simulations. We found large non-perturbative effects; in particular, the phase transition is a strongly first order one, at least up to Higgs mass of about 85 GeV. This makes electroweak baryogenesis a viable scenario with a Higgs mass not exceeding 85 GeV.

scholarly journals On the order of the QCD chiral phase transition for different numbers of quark flavours

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Francesca Cuteri ◽  
Owe Philipsen ◽  
Alessandro Sciarra
Keyword(s):  
Phase Transition ◽  
Parameter Space ◽  
Chiral Limit ◽  
Lattice Parameter ◽  
Second Order ◽  
Critical Surface ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
First Order ◽  
The Continuum

Abstract The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ $$ {N}_{\mathrm{f}}^{\ast } $$ N f ∗ ≲ 12. A reanalysis of already published $$ \mathcal{O} $$ O (a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.

scholarly journals A NEW DERIVATION OF THE COLEMAN–WEINBERG MECHANISM IN MASSLESS SCALAR QED

1996 ◽  
Vol 11 (09) ◽  
pp. 749-754 ◽  
Author(s):  
A.P.C. MALBOUISSON ◽  
F.S. NOGUEIRA ◽  
N.F. SVAITER
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Functional Integral ◽  
Massless Scalar ◽  
Integral Formalism ◽  
First Order ◽  
Unitary Gauge ◽  
Feynman Graphs ◽  
Functional Integral Formalism

We present a new derivation of the Coleman–Weinberg expression for the effective potential for massless scalar QED. Our result is obtained using the functional integral formalism, without expansions in Feynman graphs. We perform our calculations in the unitary gauge. The first-order character of the phase transition is established.

THE ELECTROWEAK PHASE TRANSITION

1992 ◽  
Vol 03 (05) ◽  
pp. 773-781 ◽  
Author(s):  
MARCELO GLEISER ◽  
EDWARD W. KOLB
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Finite Temperature ◽  
Higgs Mass ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Electroweak Model

The phase transition associated with the standard electroweak model is very weakly first order. The weakness of the transition means that around the critical temperature the finite-temperature Higgs mass is much less than the critical temperature. This leads to infrared problems in the calculation of the parameters of the potential. Therefore, theories of electroweak baryogenesis, which depend on the details of the transition, must be calculated with care.

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