Bulk Transition Line Research Articles

Critical or tricritical point in mixed-action [formula omitted] lattice gauge theory?

An analysis of scaling along the first-order bulk transition line in fundamental-adjoint SU ( 2 ) lattice gauge theory strongly supports the first-order endpoint being a tricritical point, and is inconsistent with it being an ordinary critical point as is usually assumed. If tricritical, the transition must continue from the endpoint further into the phase diagram as a second-order bulk transition and extend to and beyond the Wilson axis. Observations indicate that this is most likely the same transition that has been traditionally considered a finite-temperature transition.

Z2monopoles, vortices, and the deconfinement transition in mixed action SU(2) gauge theory

Adding separate chemical potentials $\ensuremath{\lambda}$ and $\ensuremath{\gamma}$ for ${Z}_{2}$ monopoles and vortices, respectively, in the Villain form of the mixed fundamental-adjoint action for the SU(2) lattice gauge theory, we investigate their role in the interplay between the deconfinement and bulk phase transitions using Monte Carlo techniques. Setting $\ensuremath{\lambda}$ to be nonzero, we find that the line of deconfinement transitions is shifted in the coupling plane but it behaves curiously also like the bulk transition line for large enough adjoint coupling, as for $\ensuremath{\lambda}=0.$ In a narrow range of couplings, however, we find separate deconfinement and bulk phase transitions on the same lattice for nonzero and large $\ensuremath{\lambda},$ suggesting the two to be indeed coincident in the region where a first order deconfinement phase transition is seen. In the limit of large $\ensuremath{\lambda}$ and $\ensuremath{\gamma},$ we obtain only lines of second order deconfinement phase transitions, as expected from universality.

Impact of Z2 monopoles and vortices on the deconfinement transition

Suppressing Z 2-monopoles shifts the line of deconfinement transitions in the coupling plane of the SU(2) lattice gauge theory with a mixed Villain form of action but it still continues to behave also like the bulk transition line. Separate deconfinement and bulk phase transitions are found on the same lattice, suggesting the two to be indeed coincident at higher adjoint couplings. Universality is restored when both monopoles and vortices are suppressed.

More on SU(3) lattice gauge theory in the fundamental-adjoint plane

We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with $N_t=4$, which was found to join onto the bulk transition line at its endpoint, we find that the ratio $\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the $0^{++}$ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint with the continuum limit there being a $\phi^4$ theory with a diverging correlation length only in the $0^{++}$ channel.

SU(3) lattice gauge theory in the fundamental-adjoint plane and scaling along the Wilson axis

We present further evidence for the bulk nature of the phase transition line in the fundamental-adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with N t = 4, which was found to join onto the bulk transition line at its endpoint, we find that the ratio σ T c remains approximately constant. However, the mass of the O ++ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint, with the continuum limit there being a φ 4 theory with a diverging correlation length only in the 0 ++ channel. We comment on the implications for the scaling behavior along the fundamental or Wilson axis.

Thermal phase transition in mixed action SU (3) lattice gauge theory and Wilson fermion thermodynamics

Abstract We study the thermal phase diagram of pure SU(3) lattice gauge theory with fundamental and adjoint couplings. We improve previous estimates of the position of the bulk transition line and determine the thermal deconfinement transition lines for N t = 2, 4, 6, and 8. The endpoint of the bulk transition line ( β f , β a ) = (4.00(7), 2.06(8)) improves upon earlier estimates obtained using smaller lattice sizes. For N t > 4 the deconfinement transition line splits cleanly away from the bulk transition line. With increasing N t the thermal deconfinement transition lines shift to increasingly weaker coupling, joining onto the bulk transition line at increasingly larger β a in a pattern consistent with the usual universality picture of lattice gauge theories. We also discuss the possible consequences of an induced adjoint term from the fermionic determinant and determine this induced term numerically with a microcanonical demon method for two flavors of dynamical Wilson fermions.

SU(3) lattice gauge theory with adjoint action at nonzero temperature

We study the thermal phase diagram of pure SU(3) gauge theory with fundamental and adjoint couplings. We improve previous estimates of the position of the bulk transition line and determine the thermal deconfinement transition lines for N t = 2, 4, 6, and 8. For N t > 4 the deconfinement transition line splits cleanly away from the bulk transition line. With increasing N t the thermal deconfinement transition lines shift to increasingly weaker coupling, joining onto the bulk transition line at increasingly larger β a in a pattern consistent with the usual universality picture of lattice gauge theories.

Finite-temperature phase transition in SU(2) lattice gauge theory with extended action

We study the three dimensional fundamental-adjoint SU(2) lattice gauge theory at finite temperature by Monte Carlo simulations. We find that the finite-temperature deconfinement phase transition line joins the first-order bulk phase transition line at its endpoint. Moreover, across the bulk transition line, the Polyakov loop undergoes a discontinuous jump implying the existence of both confining and deconfining phases on its two sides. Implications for universality and the nature of the confining-deconfining transition are discussed.

Surface-layer phase transitions in nematic liquid crystals.

Surface-layer transitions in nematogenic materials characterized by a preferential planar surface interaction linear in the order parameter have been studied theoretically at temperatures above the bulk transition (${\mathit{T}}_{\mathit{N}\mathit{I}}$). The coupled Euler-Lagrange nonlinear differential equations obtained from the Landau--de Gennes free energy were solved exactly by numerical integration. This problem had been studied previously employing various limits and approximations with several differences in the phase diagram reported. The exact results allow one to determine which of these differences are artifacts of the approximations used and which are dependent upon the ratio of elastic constants. It is found, for physically relevant elastic constants, that there is always a uniaxially ordered surface layer at sufficiently high temperatures. For weak surface coupling, no surface phase transition occurs and the uniaxial layer remains the stable state until ${\mathit{T}}_{\mathit{N}\mathit{I}}$ is reached. When the surface coupling is increased, there is a single first-order (prewetting) transition from uniaxial to biaxial surface ordering as the temperature is reduced towards ${\mathit{T}}_{\mathit{N}\mathit{I}}$. This transition boundary becomes second order (by way of a tricritical point) when the surface coupling is further increased. We also find that the mean-field boundary is suppressed due to Berezinskii-Kosterlitz-Thouless (BKT)--type phase fluctuations. Also, these fluctuations can result in the re-entrant (with increasing surface coupling strength) uniaxial-biaxial phase boundary terminating on the bulk transition line rather than becoming asymptotic to it.

Layering transitions in the chiral clock model: Bethe approximation

Interface phenomena, such as wetting and layering transitions of the three-state chiral clock model in three dimensions, are studied within the Bethe approximation. The Bethe approximation yields the correct sequence of first-order layering transitions. This is in contrast to the mean-field theory which is known to be qualitatively misleading for low temperatures. At higher temperatures the discontinuities of the order parameter at the layering transitions become exceedingly small so that the magnetisation profile appears to vary continuously across the interface. For finite values of the chiral field Delta the width of the interfacial layer is found to remain finite at the first-order bulk transition line. Critical wetting occurs only for Delta =0, i.e. for the symmetric three-state Potts model.