Monte Carlo study of a lattice gauge theory with a radially varied Higgs field

The phase structure of a gauge-scalar (Higgs) field system is studied by Monte Carlo simulations without freezing the radial mode of the scalar field. We consider Z₂ lattice gauge theory coupled to a Higgs field which is approximated by a discrete real one. Most of our analysis is done on a 4⁴ lattice. We find that the phase diagram of our model consists of three distinct phases, Higgs and confined regions being divided by a phase boundary. This phase structure forms a contrast with that presented in the model with a fixed-length Higgs field.     

三维Ising模型的蒙特卡罗模拟

采用蒙特卡罗(Monte Carlo)重点抽样法对三维Ising模型进行计算机模拟,测量无外磁场时三维Ising模型中自旋键链的能量、磁化强度、比热及磁化率的统计平均值与标准误差(不确定度).结果表明,三维Ising模型在无外磁场时存在自发磁化现象,铁磁→非铁磁相变临界点在J/(k_BT_C)=0.222 0,或居里温度T_C=4.500 0处.并研究存在外磁场时上述物理量随温度与外磁场的变化规律,给出物理解释.     

Finite-temperature behavior of the lattice abelian Higgs model

We study phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement. When the Higgs charge is the basic U(1) unit, we find that the Higgs and confinement regions are not separated by a phase transition and form a single homogenous phase which we call the total screening phase. The model does not undergo a symmetry restoring phase transition at finite temperature.If the Higgs charge is some multiple of the basic unit the model follows the conventional wisdom: there are 3 phases (normal, Higgs and confinement) at zero temperature, two of which disappear above some critical point. We apply the lessons learned from the lattice Higgs model to understand the behavior of the weak interactions at high temperature.In a long appendix we give an intuitive physical picture for the Polyakov-Susskind quark liberating phase transition and show that it is related to the Hagedorn spectrum of a confining model. We end with a collection of effective field theory approximations to various lattice theories.     

Abelian Higgs model with a Chern-Simons term in 3-dimensional gravitation

We consider the Abelian Higgs model with a Chern-Simons term coupled to the Einstein theory of gravitation in 3-dimensional space-time. We seek a finite solution, regular everywhere, having a stationary, cylindrically symmetric metric. We analyze these field equations and we suggest that such a solution exists. We find that the asymptotic metric of this solution corresponds to that which describes gravitationally a massive particle with spin. We obtain explicitly the expression of the spin. We give only the expression of the mass in the first order with respect to the gravitational coupling constant.     

Spontaneous symmetry breakdown in the abelian Higgs model

For the abelian Higgs model we introduce a new gauge invariant observable which in Landau gauge is . In three or more dimensions this observable is used to show that the global gauge symmetry is spontaneously broken in the lattice theory for a suitable range of parameters. This observable also provides a gauge invariant order parameter for the phase transition in this model.Research supported by U.S. National Science Foundation grant PHY8116101-A03Research supported by U.S. National Science Foundation grant PHY8117463     

A Monte Carlo study of the XY model

Spin systems which have a phase transition without an order parameter, like the XY model, have great importance in physics. Here we show how it is possible to study the behaviour of such a system by computer simulation without studying the spin-spin correlation functions.     

A Monte Carlo study of the Gross-Neveu model

Several lattice versions of the Gross-Neveu model are constructed and studied using Monte Carlo methods. The expected shiral structures are confirmed by the numerical results. The correct asymptotic freedom behaviour is recovered with the appropriate number of species taken into account. The models differ in their number of soft modes and their strong coupling behaviour. In some of them, chiral symmetry is restored at a finite coupling. The large-N, finite-temperature transition is also found in good agreement with the theoretical value.     

Phase structure of the three-dimensional radially active Abelian Higgs model

The phase diagram of the 3-D U(1) gauge-Higgs models withq=1 andq=2 are derived without freezing the Higgs field length. The models are studied for several values of λ, the Higgs self-coupling. When λ is sufficiently small, new phase transitions appear, due to the radial fluctuations.     

Monte Carlo study of the Quartet Ising model consistent with selfduality

The transition temperature obtained from recent Monte Carlo calculations for the Quartet Ising model on the fcc lattice deviated by 17% from the exact transition temperatureT _c ^SD required by selfduality which we have proven afterwards. Here we use Monte Carlo results of the internal energy, which agree well with low- and high temperature series, to determine entropy and free energy and obtain aT _c in excellent agreement (±0.1%) with the exact value. The Quartet model on the hcp lattice is shown to be selfdual too; the rapidly converging series for the fcc and the hcp lattice differ only in higher order.Guest stay     

Charged vortices in an abelian Higgs model with Chern-Simons term

The existence is shown of charged vortices of finite energy in a (2+1)-dimensional abelian Higgs model with Chern-Simons (C-S) term. Further, lower bounds on the energy and angular momentum of these vortices are obtained. Finally it is shown that the “glueballs” are absent in (2+1)-dimensional QED or QCD with C-S term for any compact gauge group.     

Monte Carlo renormalization group study of the XY model

The Δβ method has been used to investigate the phase structure of the XY model. A line of fixed points was found in the low-temperature phase, while a renormalization group trajectory (one relevant and no marginal coupling parameters) in the high-temperature phase. A study of higher (3rd and 4th) order derivatives of the free energy indicate that the phase transition is of infinite order and that hyperscaling is valid for the system.     

Worm Monte Carlo study of the honeycomb-lattice loop model

We present a Markov-chain Monte Carlo algorithm of worm   type that correctly simulates the O(n)$O(n)$ loop model on any (finite and connected) bipartite cubic graph, for any real n>0$n>0$, and any edge weight, including the fully-packed limit of infinite edge weight. Furthermore, we prove rigorously that the algorithm is ergodic and has the correct stationary distribution. We emphasize that by using known exact mappings when n=2$n=2$, this algorithm can be used to simulate a number of zero-temperature Potts antiferromagnets for which the Wang–Swendsen–Kotecký cluster algorithm is non-ergodic, including the 3-state model on the kagome lattice and the 4-state model on the triangular lattice. We then use this worm algorithm to perform a systematic study of the honeycomb-lattice loop model as a function of n?2$n?2$, on the critical line and in the densely-packed and fully-packed phases. By comparing our numerical results with Coulomb gas theory, we identify a set of exact expressions for scaling exponents governing some fundamental geometric and dynamic observables. In particular, we show that for all n?2$n?2$, the scaling of a certain return time in the worm dynamics is governed by the magnetic dimension of the loop model, thus providing a concrete dynamical interpretation of this exponent. The case n>2$n>2$ is also considered, and we confirm the existence of a phase transition in the 3-state Potts universality class that was recently observed via numerical transfer matrix calculations.     

Monte Carlo renormalization group study of φ field theory

A previously proposed general method for evaluating block renormalized coupling constants within the framework of the Monte Carlo renormalization group (MCRG) is applied to φ⁴ field theory. The flow diagrams, fixed points, and critical exponents are determined in two, three and four dimensions. Results in four dimensions are consistent with the idea that φ⁴ field theory is trivial (non-interacting) in the continuum limit. The possibility of using MCRG techniques to ascertain whether a general non-asymptotically free theory is trivial or not is also discussed.     

Effective action and cluster properties of the abelian Higgs model

We continue our program to establish the Higgs mechanism and mass gap for the abelian Higgs model in two and three dimensions. We develop a multiscale cluster expansion for the high frequency modes of the theory, within a framework of iterated renormalization group transformations. The expansions yield decoupling properties needed for a proof of exponential decay of correlations. The result of this analysis is a gauge invariant unit lattice theory with a deep Higgs potential of the shape required to exhibit the Higgs mechanism.Research partially supported by the National Science Foundation under Grant DMS-8602207 and by the Air Force Office of Scientific Research under Grant AFOSR-86-0229Alfred P. Sloan Research Fellow. Research partially supported by the National Science Foundation under Grants PHY-84-13285 and PHY-85-13554Research partially supported by the National Science Foundation under Grant PHY-85-13554     

Bond dilution in the 3D Ising model: a Monte Carlo study

We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent . According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, starting from the pure model limit down to the neighbourhood of the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions to check the stability of the disorder fixed point. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted q = 4 Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is indeed governed by the same universality class as the site-diluted model.Received: 24 February 2004, Published online: 28 May 2004PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 64.60.Fr Equilibrium properties near critical points, critical exponents - 75.10.Hk Classical spin models     

用量子蒙特卡罗方法研究二维超流-莫特绝缘体相变点附近的希格斯粒子

与伽利略不变性的超流体不同, 具有洛伦兹不变性的超流体中除了声子模之外, 还存在希格斯振幅模(Higgs amplitude mode). 在二维情况下, 由于存在十分剧烈的衰变成声子模的过程, 希格斯模是否仍然是一个能产生尖锐线性响应的激发子成为了一个问题. 近年来的进展最终对这一持续数十年的争论做出了肯定的回答, 证实了希格斯的可观测性. 在这里, 我们回顾一系列的数值方面的工作; 它们以二维超流体(superfluid)到莫特绝缘体(Mott insulator) 量子相变点(SF-MI QCP) 附近的具有洛伦兹不变性的超流体为对象, 成功探测到了希格斯模的线性响应信号. 特别是, 我们介绍了一种如何使用平衡态系统的蒙特卡罗算法计算强关联系统的延迟响应函数(retarded response function)的方法. 该方法主要包含两个核心步骤: 即通过路径积分表示下的蠕虫算法这一高效的蒙特卡罗算法计算平衡态系统的虚时间关联函数, 然后利用数值解析延拓方法从虚时间关联函数中获得实时间(实频率)的响应函数. 将该数值方法应用于二维SF-MI QCP附近的玻色-哈伯德模型(Bose-Hubbard Model), 结果表明尽管在超流相中, 希格斯模衰变过程非常剧烈, 但是在动能算符相对应的延迟响应函数的虚部中, 仍然可以观测到希格斯模所对应的尖锐的共振峰. 进一步的研究表明, 在莫特绝缘相, 甚至常流体相中, 也可能存在类似的共振峰信号. 由于可以在光晶格中超冷原子系统等凝聚态中观测到SF-MI QCP, 因此希格斯共振峰有望通过实验进行直接探测. 此外我们指出, 同样的希格斯共振峰还存在于所有和SF-MI QCP具有相同普适类((2+1)维相对论性U(1)临界性)的量子临界系统中.     

Monte Carlo Study of 3-d Z4 Gauge-Z2 Higgs Theory with Radial Degree of Freedom

Phase structure of the 3-d lattice Z₄ gauge-Z₂ Higgs theory is investigated by the Monte Carlo simulation. We find a new phase, named Higgs Ⅱ phaae, when λ (scalar self-coupling constant) is small. It is a result of the radial excitation of Higgs field.