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Attila Nagy

Publications and source records attributed to Attila Nagy.

At least 37 records · Page 2Linked to original sources
arXiv2016

Finite Size Scaling of the Higgs-Yukawa Model near the Gaussian Fixed Point

We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility study of our strategy is performed for the pure scalar theory in the weak-coupling regime. Choosing the on-shell renormalisation scheme gives us an advantage to fit the scaling functions against lattice data with only a small number of fit parameters. These formulae can be used to determine the universality of the observed phase transitions, and thus play an essential role in future investigations of Higgs-Yukawa models, in particular in the strong Yukawa coupling region.

hep-lat↗
arXiv2016

Remarks on the paper "M. Kolibiar, On a construction of semigroups"

In his paper "On a construction of semigroups", M. Kolibiar gives a construction for a semigroup $T$ (beginning from a semigroup $S$) which is said to be derived from the semigroup $S$ by a $θ$-construction. He asserted that every semigroup $T$ can be derived from the factor semigroup $T/θ(T)$ by a $θ$-construction, where $θ(T)$ is the congruence on $T$ defined by: $(a, b)\in θ(T)$ if and only if $xa=xb$ for all $x\in T$. Unfortunately, the paper contains some incorrect part. In our present paper we give a revision of the paper.

math.GR↗
arXiv2015

A Note on Semigroup Algebras of Permutable Semigroups

Let $S$ be a semigroup and $\mathbb F$ be a field. For an ideal $J$ of the semigroup algebra ${\mathbb F}[S]$ of $S$ over $\mathbb F$, let $\varrho _J$ denote the restriction (to $S$) of the congruence on ${\mathbb F}[S]$ defined by the ideal $J$. A semigroup $S$ is called a permutable semigroup if $α\circ β=β\circ α$ is satisfied for all congruences $α$ and $β$ of $S$. In this paper we show that if $S$ is a semilattice or a rectangular band then $φ_{\{S;{\mathbb F}\}}:\ J\mapsto \varrho _J$ is a homomorphism of the semigroup $(Con ({\mathbb F}[S]);\circ )$ into the relations semigroup $({\cal B}_S; \circ )$ if and only if $S$ is a permutable semigroup.

math.RA↗
arXiv2015

On Congruences on Ultraproducts of Algebraic Structures

Let $I$ be a non-empty set and $\mathcal{D}$ an ultrafilter over $I$. For similar algebraic structures $B_i$, $i\in I$ let $Π(B_i|i\in I)$ and $Π_{\mathcal{D}}(B_i|i\in I)$ denote the direct product and the ultraproduct of $B_i$, respectively. Let $\mathcal{D}^*$ denote the ultraproduct congruence on $Π(B_i|i\in I)$. Let the $\wedge$-semilattice of all congruences on an algebraic structure $B$ denoted by ${\bf Con}(B)$. In this paper we show that, for any similar algebraic structures $A_i$, $i\in I$, there is an embedding $Φ$ of $Π_{\mathcal{D}}({\bf Con}(A_i)|i\in I)$ into ${\bf Con}(Π_{\mathcal{D}}(A_i|i\in I)$. We also show that, for every $σ\in Π({\bf Con}(A_i)|i\in I)$, the factor algebra $Π_{\mathcal{D}}(A_i|i\in I)/Φ(σ/\mathcal{D}^*)$ is isomorphic to $Π_{\mathcal{D}}(A_i/σ(i)|i\in I)$. Moreover, if $A$ is an algebraic structure, $σ(i)\in {\bf Con}(A)$, $i\in I$ and $\mathcal{D}=\{ K_j| j\in J\}$ then the restriction of $Φ(σ/\mathcal{D}^*)$ to $A$ equals $\vee _{j\in J}(\wedge _{k\in K_j}σ(k))$.

math.CT↗
arXiv2015

Lattice study of the Higgs-Yukawa model in and beyond the Standard Model

We derive finite-size scaling formulae for four-dimensional Higgs-Yukawa models near the Gaussian fixed point. These formulae will play an essential role in future, detailed investigation of such models. In particular, they can be used to determine the nature of the observed phase transitions, and confirm or rule out the possibility of having non-trivial fixed points in the Higgs-Yukawa models. Our scaling formula for Binder's cumulant is tested against lattice simulations carried out at weak couplings, and good agreement is found. As a separate project, we also present preliminary results from our study of a chirally-invariant Higgs-Yukawa model including a dimension-six operator at finite temperature. Our work provides first indications of first-order temperature-induced phase transitions near the infinite cutoff limit in this model.

hep-lat↗
arXiv2015

On Special Semigroups Derived From an Arbitrary Semigroup

Let $S$ be a semigroup, $Λ$ a non-empty set and $P$ a mapping of $Λ$ into $S$. The set $S\times Λ$ together with the operation $\circ _P$ defined by $(s, λ)\circ _P(t, μ)=(sP(λ)t, μ)$ form a semigroup which is denoted by $(S, Λ, \circ _P)$. Using this construction, we prove a common connection between the semigroups $S$, $S/θ$ and $S/θ^*=(S/θ)/(θ^*/θ)$, where $θ$ and $θ^*/θ$ are the kernels of the right regular representations of $S$ and $S/θ$, respectively. We also prove an embedding theorem for the semigroup $(S, S/θ, \circ _p)$, where $S$ is a left equalizer simple semigroup without idempotents, and $P$ maps every $θ$-class of $S$ into itself.

math.GR↗
arXiv2015

Retractable state-finite automata without outputs

A homomorphism of an automaton ${\bf A}$ without outputs onto a subautomaton ${\bf B}$ of ${\bf A}$ is called a retract homomorphism if it leaves the elements of $B$ fixed. An automaton ${\bf A}$ is called a retractable automaton if, for every subautomaton ${\bf B}$ of ${\bf A}$, there is a retract homomorphism of ${\bf A}$ onto ${\bf B}$. In [1] and [3], special retractable automata are examined. The purpose of this paper is to give a complete description of state-finite retractable automata without outputs.

cs.FL↗
arXiv2015

Left equalizer simple semigroups

In this paper we characterize and construct semigroups whose right regular representation is a left cancellative semigroup. These semigroups will be called left equalizer simple semigroups. For a congruence $\varrho$ on a semigroup $S$, let ${\mathbb F}[\varrho]$ denote the ideal of the semigroup algebra ${\mathbb F}[S]$ which determines the kernel of the extended homomorphism of ${\mathbb F}[S]$ onto ${\mathbb F}[S/\varrho]$ induced by the canonical homomorphism of $S$ onto $S/\varrho$. We examine the right colons $({\mathbb F}[\varrho]:_r{\mathbb F}[S])=\{ a\in {\mathbb F}[S]:\ {\mathbb F}[S]a\subseteq {\mathbb F}[\varrho ]\}$ in general, and in that special case when $\varrho$ has the property that the factor semigroup $S/\varrho$ is left equalizer simple.

math.GR↗
arXiv2015

Separators of Ideals in Multiplicative Semigroups of Unique Factorization Domains

In this paper we show that if $I$ is an ideal of a commutative semigroup $C$ such that the separator $SepI$ of $I$ is not empty then the factor semigroup $S=C/P_I$ ($P_I$ is the principal congruence on $C$ defined by $I$) satisfies Condition $(*)$: $S$ is a commutative monoid with a zero; The annihilator $A(s)$ of every non identity element $s$ of $S$ contains a non zero element of $S$; $A(s)=A(t)$ implies $s=t$ for every $s, t\in S$. Conversely, if $α$ is a congruence on a commutative semigroup $C$ such that the factor semigroup $S=C/α$ satisfies Condition $(*)$ then there is an ideal $I$ of $C$ such that $α=P_I$. Using this result for the multiplicative semigroup $D_{mult}$ of a unique factorization domain $D$, we show that $P_{J(m)}=τ_m$ for every nonzero element $m\in D$, where $J(m)$ denotes the ideal of $D$ generated by $m$, and $τ_m$ is the relation on $D$ defined by $(a, b)\in τ_m$ if and only if $gcd(a, m)\sim gcd(b, m)$ ($\sim$ is the associate congruence on $D_{mult}$). We also show that if $a$ is a nonzero element of a unique factorization domain $D$ then $d(a)=|D'/P_{J([a])}|$, where $d(a)$ denotes the number of all non associated divisors of $a$, $D'=D/\sim$, and $[a]$ denotes the $\sim$-class of $D_{mult}$ containing $a$. As an other application, we show that if $d$ is one of the integers $-1$, $-2$, $-3$, $-7$, $-11$, $-19$, $-43$, $-67$, $-163$ then, for every nonzero ideal $I$ of the ring $R$ of all algebraic integers of an imaginary quadratic number field ${\mathbb Q}[\sqrt d]$, there is a nonzero element $m$ of $R$ such that $P_I=τ_m$.

math.GR↗
arXiv2015

Notes on a problem on weakly exponential $Δ$-semigroups

A semigroup $S$ is called a weakly exponential semigroup if, for every couple $(a,b)\in S\times S$ and every positive integer $n$, there is a non-negative integer $m$ such that $(ab)^{n+m}=a^nb^n(ab)^m=(ab)^ma^nb^n$. A semigroup $S$ is called a $Δ$-semigroup if the lattice of all congruences of $S$ is a chain with respect to inclusion. The weakly exponential $Δ$-semigroups were described in [5]: A. Nagy, Weakly exponential $Δ$-semigroups, Semigroup Forum, 40(1990), 297-313. Although the existence of two types of them (T2R and T2L semigroups) is an open question, Theorem 3.11 of [5] gives necessary and sufficient conditions for a semigroup to be a T2R [T2L] semigroup. In our present paper we give a little correction of condition (v) of Theorem 3.11 of [5], and prove some new results which are addendum to the problem: Doest there exist a T2R [T2L] semigroup?

math.GR↗
arXiv2015

The separator of a subset of a semigroup

In this paper we introduce a new notion by the help of the idealizer. This new notion is the separator of a subset of a semigroup. We investigate the properties of the separator in an arbitrary semigroup and characterize the unitary subsemigroups and the prime ideals by the help of their separator. The last section of this paper treats the separator of a free subsemigroup of a free semigroup.

math.GR↗
arXiv2015

A lattice study of a chirally invariant Higgs-Yukawa model including a higher dimensional $Φ^6$-term

We discuss the non-thermal phase structure of a chirally invariant Higgs-Yukawa model on the lattice in the presence of a higher dimensional $Φ^6$-term. For the exploration of the phase diagram we use analytical, lattice perturbative calculations of the constraint effectice potential as well as numerical simulations. We also present first results of the effects of the $Φ^6$-term on the lower Higgs boson mass bounds.

hep-lat↗
arXiv2015

On Monoid Congruences of Commutative Semigroups

In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the help of subsets A of S whose separator is not empty.

math.GR↗
arXiv2015

On Commutative Monoid Congruences of Semigroups

A subset A of a semigroup S is called a medial subset of S if xaby is in A if and only if xbay is in A for every elements x, y, a, b of S. In the paper we show how we can construct the commutative monoid congruences of a semigroup S by the help of medial subsets of S.

math.GR↗
arXiv2015

Reflexive Unitary Subsemigroups of Left Simple Semigroups

Ideal series of semigroups play an important role in the examination of semigroups which have proper two-sided ideals. But the corresponding theorems cannot be used when left simple (or right simple or simple) semigroups are considered. So it is a natural idea that we try to use the group theoretical methods (instead of the ring theoretical ones) for the examination of these semigroups. The purpose of this paper is to find a suitable type of subsemigroups of left simple semigroups which makes possible for us to generalize some notions (the notion of the normal series and the composition series of groups) and some results concerning the groups to the left simple semigroups. We note that the subsemigroups we are looking for are the reflexive unitary subsemigroups of left simple semigroups.

math.GR↗
arXiv2015

Phase structure and Higgs boson mass in a Higgs-Yukawa model with a dimension-6 operator

We investigate the impact of a $λ_6 φ^6$ term included in a chirally invariant lattice Higgs-Yukawa model. Such a term could emerge from BSM physics at some larger energy scale. We map out the phase structure of the Higgs-Yukawa model with positive $λ_6$ and negative quartic self coupling of the scalar fields. To this end, we evaluate the constraint effective potential in lattice perturbation theory and also determine the magnetization of the model via numerical simulations which allow us to reach also non-perturbative values of the couplings. As a result, we find a complex phase structure with first and second order phase transitions identified through the magnetization. Further we analyze the effect of such a $φ^6$ term on the lower Higgs boson mass bound to see, whether the standard model lower mass bound can be altered.

hep-lat↗
arXiv2014

Finite Permutable Putcha Semigroups

A semigroup $S$ is called a permutable semigroup if $α\circ β=β\circ α$ is satified for all congruences $α$ and $β$ of $S$. A semigroup is called a Putcha semigroup if it is a semilattice of archimedean semigroups. In this paper we deal with finite permutable Putcha semigroups. We describe the finite permutable archimedean semigroups and finite permutable semigroups which are semilattices of a group and a nilpotent semigroup.

math.GR↗