scholarly journals Simulating the scalar field on the fuzzy sphere

2005 ◽  
Author(s):  
Fernando Garcia Flores ◽  
Denjoe O'Connor ◽  
X. Martin
Keyword(s):  
Scalar Field ◽  
Fuzzy Sphere

scholarly journals DIFFERENTIAL CALCULUS ON FUZZY SPHERE AND SCALAR FIELD

1998 ◽  
Vol 13 (19) ◽  
pp. 3235-3243 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Scalar Field ◽  
Dirac Operator ◽  
Differential Calculus ◽  
Spectral Triple ◽  
Fuzzy Sphere ◽  
Alternative Possibility ◽  
Operator Ordering

We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define Connes' spectral triple on the fuzzy sphere and the differential calculus. The differential calculus based on this new spectral triple is simplified considerably. Using this formulation the action of the scalar field is derived.

Simulating the scalar field using the fuzzy sphere

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2389-2396 ◽  
Author(s):  
XAVIER MARTIN
Keyword(s):  
Scalar Field ◽  
Numerical Scheme ◽  
Approximation Scheme ◽  
Fuzzy Sphere ◽  
Continuous Space ◽  
The Real ◽  
Matrix Algebras ◽  
Real Scalar ◽  
Fuzzy Space ◽  
Commutative Matrix

Fuzzy spaces provide a new approximation scheme using (non–commutative) matrix algebras to approximate the algebra of function of the continuous space. This paper describes how to implement a numerical scheme based on a fuzzy space approximation. In this first attempt, the simplest fuzzy space and field theory, respectively the fuzzy two–sphere and the real scalar field, are used to simulate the real scalar field on the plane. Along the way, this method is compared to its traditional lattice discretisation equivalent.

scholarly journals TOPOLOGICAL STABILITY OF BROKEN SYMMETRY ON FUZZY SPHERES

2012 ◽  
Vol 27 (14) ◽  
pp. 1250082 ◽  
Author(s):  
S. DIGAL ◽  
T. R. GOVINDARAJAN
Keyword(s):  
Scalar Field ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Broken Symmetry ◽  
Fuzzy Sphere ◽  
Topological Stability

We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere [Formula: see text]. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform configuration which diverge, due to Mermin–Wagner–Hohenberg–Coleman theorem, leading to the decay of the condensate. Interesting implications of enhanced topological stability of the configurations are pointed out.

scholarly journals FINITE TEMPERATURE PHASE TRANSITION OF A SCALAR FIELD ON A FUZZY SPHERE

2008 ◽  
Vol 23 (21) ◽  
pp. 1781-1791 ◽  
Author(s):  
C. R. DAS ◽  
S. DIGAL ◽  
T. R. GOVINDARAJAN
Keyword(s):  
Phase Transition ◽  
Scalar Field ◽  
Finite Temperature ◽  
Zero Mode ◽  
Temperature Phase ◽  
Fuzzy Sphere ◽  
Stable States ◽  
First Order ◽  
Auto Correlation ◽  
Temperature Phase Transition

We study finite temperature phase transition of neutral scalar field on a fuzzy sphere using Monte Carlo simulations. We work with the zero mode in the temporal directions, while the effects of the higher modes are taken care by the temperature dependence of r. In the numerical calculations we use "pseudo-heatbath" method which reduces the auto-correlation considerably. Our results agree with the conventional calculations. We report some new results which show the presence of meta-stable states, first order symmetry breaking transition and existence of multiple triple points in the phase diagram..

scholarly journals Triple point of a scalar field theory on a fuzzy sphere

2018 ◽  
Vol 2018 (10) ◽  
Author(s):  
Samuel Kováčik ◽  
Denjoe O’Connor
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Triple Point ◽  
Fuzzy Sphere ◽  
Scalar Field Theory

scholarly journals SPONTANEOUS SYMMETRY BREAKDOWN IN FUZZY SPHERES

2009 ◽  
Vol 24 (33) ◽  
pp. 2693-2701 ◽  
Author(s):  
C. R. DAS ◽  
S. DIGAL ◽  
T. R. GOVINDARAJAN
Keyword(s):  
Scalar Field ◽  
Global Symmetry ◽  
Fuzzy Sphere ◽  
Complex Scalar ◽  
Nonlocal Interactions ◽  
Symmetry Breakdown ◽  
Complex Scalar Field ◽  
Goldstone Modes ◽  
Spontaneous Symmetry Breakdown

We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal interactions present in these through geometrical considerations.

scholarly journals Entanglement entropy in scalar field theory on the fuzzy sphere

2016 ◽  
Vol 2016 (2) ◽  
pp. 023B03 ◽  
Author(s):  
Shizuka Okuno ◽  
Mariko Suzuki ◽  
Asato Tsuchiya
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Entanglement Entropy ◽  
Fuzzy Sphere ◽  
Scalar Field Theory

scholarly journals NONCOMMUTATIVE FIELD THEORY: NUMERICAL ANALYSIS WITH THE FUZZY DISK

2012 ◽  
Vol 27 (24) ◽  
pp. 1250137 ◽  
Author(s):  
FEDELE LIZZI ◽  
BERNARDINO SPISSO
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Rotation Group ◽  
Intimate Relationship ◽  
Noncommutative Field Theory ◽  
Fuzzy Sphere ◽  
Scalar Field Theory ◽  
Algebra Of Functions ◽  
The Matrix ◽  
Transition Curves

The fuzzy disk is a discretization of the algebra of functions on the two-dimensional disk using finite matrices which preserves the action of the rotation group. We define a φ4 scalar field theory on it and analyze numerically three different limits for the rank of the matrix going to infinity. The numerical simulations reveal three different phases: uniform and disordered phases already present in the commutative scalar field theory and a nonuniform ordered phase as noncommutative effects. We have computed the transition curves between phases and their scaling. This is in agreement with studies on the fuzzy sphere, although the speed of convergence for the disk seems to be better. We have also performed the limits for the theory in the cases of the theory going to the commutative plane or commutative disk. In this case the theory behaves differently, showing the intimate relationship between the nonuniform phase and noncommutative geometry.

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